President Bush, in the Mideast to push along a peace deal by the end of his presidency, gave orders to both sides on Wednesday. He told Israelis that "illegal" settlement outposts in disputed land must go and told Palestinians that no part of their territories can be "a safe haven for terrorists."

On that, Bush was echoing his ally and host, Israeli Prime Minister Ehud Olmert, who said in their joint news conference that "there will be no peace" unless attacks are halted from all parts of the Palestinian territories, including those not controlled by his negotiating partners in the Palestinian leadership. Olmert, however, said that both sides "are very seriously trying to move forward" on a peace agreement.

"Israel does not tolerate and will not tolerate the continuation of these vicious attacks," Olmert said, after two and a half hours of talks with Bush that made him uncharacteristically late for their appearance. "We will not hesitate to take all the necessary measures. There will be no peace unless terror is stopped. And terror will have to be stopped everywhere."

On Wednesday, Israeli strikes in the Gaza Strip killed one militant and two civilians, according to Palestinian medics. The Israeli army said the attacks were needed because Palestinian militants had bombarded the rocket-scarred southern Israeli city of Sderot with rocket and mortar fire. Two houses in Sderot were struck, but there were no injuries.

On the first day of his eight-day Mideast trip aimed at encouraging a long-elusive Israeli-Palestinian agreement, Bush said: "I'm under no illusions. This is going to be hard work."

Bush said he and Olmert also discussed Iran's nuclear weapons ambitions and an incident Sunday when Iranian boats harassed and provoked three American Navy ships in the strategic Strait of Hormuz. U.S. officials said Iran threatened to explode the vessels, but the incident ended peacefully.

The president said "all options are on the table to secure our assets." He said serious consequences would follow another Iranian provocation. "My advice to them is don't do it," he said.

Bush found himself challenged by his Israeli allies on a recent U.S. intelligence report saying Iran halted a nuclear weapons program in 2003. Tehran's nuclear ambitions are a chief fear in Israel, and the U.S. report led some in the region _ both Israelis and Arab nations concerned about rising Iranian influence _ to doubt the U.S. commitment to reining in Tehran. The report also undercut U.S. efforts to build support for sanctions against Iran.

"The fact that they suspended the program was heartening," Bush said. "The fact that they had one was discouraging because they could restart it."

Clearing up confusion about U.S. policy toward Iran is a key subtext of Bush's trip, which will also take him to Kuwait, Bahrain, United Arab Emirates, Saudi Arabia and Egypt. Bush visits Palestinian President Mahmoud Abbas Thursday in the West Bank, a Palestinian territory. But he will not stop in or near the Gaza Strip, the other Palestinian territory which is controlled by Islamic Hamas militants who are not a party to negotiations. It was from Gaza that militants launched rockets Wednesday into southern Israel and where Palestinian hard-liners staged a small anti-Bush protest.

The president's national security adviser, Stephen Hadley, said the people of Gaza must at some point decide what kind of future they want and whether they want Hamas in charge. Such decisions will play a big role in what sort of Palestinian state can be created. "At this point, it's a pretty depressing situation," Hadley said of the split in Palestinian control.

Bush's arrival in Israel came amid ongoing land squabbles and fears of violence. There's been little headway since he hosted a splashy Mideast conference in November in Annapolis, which launched the first major peace talks in seven years.

But Olmert, despite his tough words on terror, spoke optimistically.

"Your visit is timely and is very important to encourage the process that you and Secretary Rice helped start in Annapolis few weeks ago and that we, both sides I believe are very seriously trying to move forward with now in order to realize the vision of a two-state solution," the Israeli leader said.

Bush said he believes both Olmert and Abbas "are determined to make the hard choices necessary."

"Am I nudging them forward? Well, my trip was a pretty significant nudge because yesterday they had a meeting," he said.

On the eve of Bush's arrival, Olmert and Abbas pledged to have negotiators begin work immediately on the so-called final status issues. These include the final borders between Israel and a future Palestine, completing claims to the holy city of Jerusalem, the fate of millions of Palestinian refugees and Israeli security concerns.

Bush and his team stepped into a tricky issue _ Palestinian anger about Israeli plans to build new housing in east Jerusalem and the West Bank. Those areas were captured by Israel in the 1967 Mideast war and are claimed by the Palestinians for their future state.

Secretary of State Condoleezza Rice said that Israeli construction in Palestinian-claimed east Jerusalem constitutes settlement activity and is opposed by the U.S. Rice's comments, published in The Jerusalem Post daily, marked the U.S. administration's strongest criticism yet of Israeli policies in disputed east Jerusalem. The Palestinians are expected to put settlements at the top of their agenda for their meetings with Bush.

Bush didn't go as far as Rice, but said of unauthorized Jewish outposts in the West Bank: "The agreement was get rid of outposts -- illegal outposts. And they ought to go."

OImert said Israel "must abide by our commitments and we shall do so."

Abbas adviser Nabil Amr said Bush's settlement comments were generally positive. "But we expected him to say that we don't want any more settlement activity, because the Israelis are using the tactic of not building new settlements, but enlarging the current ones, and this is dangerous," he said.

Amr said the United States needs to push, not coax, Israel. "Israel is not willing to provide anything without pressure, and the pressure has to come from the U.S.," he said.

Bush also indicated a willingness to address Israel's concerns with the Palestinians.

Upon arrival at the airport, he lent support to Israel on one of the core issues in the conflict. "The alliance between our two nations helps guarantee Israel's security as a Jewish state," Bush said.

Bush has referred to Israel as Jewish state in the past but the reference _ here in the region _ had special significance. Palestinians oppose the term, saying it rules out the right of Palestinian refugees to return to lost properties in Israel.

And in the news conference with Olmert, Bush said he would tell Abbas that his territory "cannot be a safe haven for terrorists."

Israel has demanded that Palestinian forces do more to stop militants not just in Gaza, but in the West Bank. Since Olmert and Abbas last met, two Israelis were killed in the West Bank, and Israeli security forces say members of Abbas' Fatah movement were responsible.

It is Bush's first presidential visit to Israel. Unpopular at home, he was greeted here with smiles and warm handshakes.

Bush's first formal meeting was with Israeli President Shimon Peres, at his official residence. Peres said the Annapolis conference started a one-year clock on the difficult Mideast peace process, underscoring Bush's hopes _ considered unrealistic by many in the Mideast and the United States _ to conclude a deal before he leaves office. "Time is so precious," Peres said.