JERUSALEM — After a morning of heavy rocket fire from Gaza into Israel, the Israeli military seemed to be edging closer to a ground invasion of Gaza on Friday, saying forces were “on standby” and “ready to enter should it be decided that a ground operation is necessary.”

In a statement, the Israeli military said paratrooper and infantry brigades had completed final preparations for a potential ground operation, which would be the first since the winter of 2008-09, when Israel drew broad international reproach for an invasion that claimed 1,400 Palestinian lives for the loss of 13 Israelis.

The statement came after scores of rockets were fired into Israel, striking major cities of the south, causing widespread panic and damage and shattering plans for a temporary cease-fire during a remarkable visit to Gaza by the Egyptian prime minister that showed the shifting dynamics of Middle East politics since the turmoil of the Arab Spring uprisings.

Word of the potential invasion emerged shortly before a rocket from Gaza struck near Tel Aviv. It was the second attempt to strike at the city in two days. Hamas said it had fired a single “homemade” projectile toward Tel Aviv.

An Israeli police spokesman, Micky Rosenfeld, said the rocket that was fired at Tel Aviv probably landed in the sea, and that it was one of about 120 rockets fired into Israel by dusk on Friday. Israeli officials say that the only rockets in Gaza with a range that can reach Tel Aviv are Iranian-made Fajr-5 projectiles that Israel has been trying to take out with hundreds of airstrikes over the last two days.

The fact that these rockets were still being fired seemed to weigh heavily in Israeli military calculations about a ground invasion. After a meeting with President Shimon Peres, Prime Minister Benjamin Netanyahu said that the Israeli army was “continuing to hit Hamas hard and is ready to expand the operation into Gaza,” according to a statement from his office.

Mr. Netanyahu said that the aim was “to take out the terrorist infrastructure in Gaza while doing everything possible not to harm civilians.” He added that “Israel must continue to hit hard the missiles which are intended for central and southern Israel.”

The rapidly escalating confrontation between Hamas and Israel followed an Israeli airstrike on Wednesday that killed the top commander of Hamas, and the tit-for-tat violence is widely seen as a potential catalyst for broader hostilities at a time of spreading turmoil in Syria and elsewhere in the region.

The Israeli military said Col. Amir Baram, commander of the Israel Defense Forces’ paratroopers brigade, had addressed his forces during a preparatory briefing in the field, saying: “We are already 48 hours into an operation that we knew would have to happen. We have spoken about it during training, exercises and conferences. There is now no doubt that we have to operate. This is why we enlisted, and why we have trained.”

Witnesses on the Gaza-Israel border said Israeli tanks had massed in several places.

Early on Friday, the Israeli military said it had called up 16,000 army reservists after Defense Minister Ehud Barak authorized the call-up of 30,000 reservists, if needed, to move against what Israel considers an unacceptable security threat from smuggled rockets amassed by Hamas, which does not recognize Israel’s right to exist.

It was not initially clear whether the show of Israeli force on the ground was meant as more of an intimidation tactic to further pressure Hamas leaders, who had all been forced into hiding on Wednesday after the group’s military chief, Ahmed al-Jabari, was killed in a pinpoint aerial bombing. But Israel’s preparations seemed to pick up on Friday after the attempts to land rockets in Tel Aviv added new urgency while Hamas itself seemed emboldened by Egypt’s support.

“The time in which the Israeli occupation does whatever it wants in Gaza is gone,” said Ismail Haniya, the Hamas prime minister.

Initially, the Egyptian initiative was portrayed as a potential harbinger of reduced hostilities, and, as Prime Minister Hesham Qandil of Egypt prepared to travel to Gaza, Israel agreed to a temporary conditional cease-fire for the visit. But the truce never took root.

Israel Radio said Palestinian militants had fired 25 rockets into southern Israel, one of them striking a house. There were no immediate reports of casualties.

What sounded like airstrikes by Israeli F-16s were also audible in Gaza City. The Israeli military said no such strikes had taken place, but the Hamas Health Ministry reported that two people, including a child, were killed in the north of Gaza City while the Egyptian delegation was on the ground,.

The Palestinian death toll rose to 23 on Friday. Three Israelis were killed Thursday in a rocket attack in Kiryat Malachi, a small town in southern Israel, when a rocket fired from Gaza struck their apartment building. Mr. Qandil’s visit produced dramatic imagery to underpin the Egyptian government’s support for Hamas, which Israel, the United States and much of the West consider to be a terrorist organization.

Mr. Qandil and Mr. Haniya visited the Al Shifa hospital amid a huge scrum of bodyguards and journalists, saying they had carried the body of Mohammed Yasser, one of eight children who Palestinian health officials say have been killed in the surge of violence since a top Hamas commander was killed in an Israeli airstrike on Wednesday.

“This is the blood of our children on our clothes,” Mr. Haniya said as he showed spatters on his clothing, “These are the Egyptian and the Palestinian blood united together.”

Like President Mohamed Morsi of Egypt on Thursday, Mr. Qandil walked a delicate line between support for Hamas, condemnation of Israel and a quest for calm in a region increasingly threatened by the spillovers from Syria’s civil war, as well as by the long-festering impasse between the Israelis and Palestinians.

“The aim of this visit is not only to show political support but to support the Palestinian people on the ground,” Mr. Qandil said, noting that he had brought with him a delegation from the Egyptian Health Ministry. He said a cease-fire between Gaza and Israel was “the only way to achieve stability in the region” and also called on the Palestinians to repair the rift between Hamas in Gaza and the Fatah group that dominates the Palestinian Authority in the West Bank. “We call on the Palestinian people to unite because their power and strength is in their unity,” Mr. Qandil said. “That’s the only way to liberate Palestine.”

The visit was the first of such a high-ranking Egyptian official to this coastal enclave since the militant Hamas faction gained control in 2007 and offered a potent sign of how Egypt’s revolution and new Islamist leadership since the overthrow of President Hosni Mubarak last year has shifted the geopolitics of the Israeli-Palestinian conflict.

Egypt, Mr. Qandil said, will “save nothing to stop the aggression and achieve a continuous cease-fire on the way to having a Palestinian state with Jerusalem as its capital.”

Mr. Haniya said: “Egypt cannot accept the aggression as before. I welcome Egypt for this historical visit that comes in harmony with the will of the free Egypt.”

Before the visit, residents in Gaza said the night was filled with the boom and crash of airstrikes, with loud explosions at dawn on Friday, a day after Israel and the Hamas rulers of Gaza brushed aside international calls for restraint and escalated their lethal conflict.

In Gaza, Palestinian militants launched hundreds of rockets into Israeli territory on Thursday, targeting Tel Aviv for the first time, and Israel intensified its aerial assaults.

Defense Minister Barak, expressing outrage over two long-range Palestinian rockets that whizzed toward Tel Aviv on Thursday and set off the first air-raid warning in the Israeli metropolis since it was threatened by Iraqi Scud missiles in the Persian Gulf war of 1991, said, “There will be a price for that escalation that the other side will have to pay.”

Within hours of the Tel Aviv air-raid warning, the Israel Defense Forces said that they had attacked 70 underground rocket-launching sites in Gaza and that “direct hits were confirmed.” At the same time, Israel signaled its concern to preserve its so-called cold peace with Egypt, with Mr. Netanyahu agreeing to the temporary cease-fire during the visit of Prime Minister Qandil, who also met briefly with the Hamas cabinet.

An official in Mr. Netanyahu’s office said by telephone that Israel had told Egypt that the cease-fire would hold as long as “there would not be hostile fire from the Gaza Strip into Israel.”

“Prime Minister Netanyahu is committed to the peace treaty with Egypt,” the official said. “That peace serves the strategic interests of both countries.” There was no suggestion that the Israelis were considering a more permanent cease-fire at this stage.

Overnight, Israel said it launched 150 airstrikes while Palestinians fired a dozen rockets into Israel — far fewer than the hundreds that have hurtled toward Israel in the past two days.

Military officials said Israel’s aerial assaults had hit more than 450 sites in Gaza by early Friday. The officials also said that militants in Gaza had fired more than 300 rockets into southern Israel since Wednesday and that at least 130 more had been intercepted by Israel’s Iron Dome antimissile defense system.

In Tel Aviv on Thursday, one rocket crashed into the sea off its coast and another apparently fell short. But the ability of militants 40 miles away to fire those weapons at the city of 400,000 underscored, in the Israeli government’s view, the justification for the intensive aerial assaults on hundreds of suspected rocket storage sites and other targets in Gaza.

In Washington, Obama administration officials said they had asked friendly Arab countries with ties to Hamas to use their influence to seek a way to defuse the hostilities. At the same time, however, a State Department spokesman, Mark C. Toner, reiterated to reporters the American position that Israel had a right to defend itself from the rocket fire and that the “onus was on Hamas” to stop it.