Israel slowed its withdrawal of forces from Gaza on Tuesday as the two-day cease-fire with Hamas suffered its first violations. Israeli troops twice came under fire, and eight mortar shells were shot at Israel, all falling short. Israel responded with airstrikes on launching sites.

Thousands of Palestinians supported Hamas at four rallies here while the United Nations secretary general, Ban Ki-moon, visited to express support for those who had suffered in the war. An Arab meeting in Kuwait aimed at helping Gaza ended in disarray.

Israel would not comment on the pace of withdrawal, but Israel Radio’s military affairs correspondent reported that some soldiers held positions in northern Gaza to make sure Hamas did not retake rocket-launching sites.

Israeli gunboats offshore occasionally fired warning shots at boats that ventured too close.

Both sides declared unilateral cease-fires during the weekend after a three-week Israeli assault aimed at stopping years of rocket fire, but the way forward remains murky. Hamas said Israel had seven days to leave; Israel said it would leave on its own schedule, and only if Hamas stopped firing.

Mr. Ban, the highest-ranking international figure to come to Gaza since the war, visited the United Nations compound, damaged by an Israeli strike. He called the attack “outrageous” and demanded an investigation. He said Israel had used excessive force in Gaza. After touring the area, Mr. Ban called the destruction “shocking and alarming.”

Later, he visited Sderot, the southern Israeli town that has long borne the brunt of Hamas rocket fire, and said using rockets against civilians violated international law. Still, he said, Israel should lift its border closing on Gaza, strangling its economy.

The pro-Hamas rallies in Gaza, in four cities, produced a blaze of green Hamas flags as marchers walked past the devastation from Israeli air raids. In Gaza City, the march passed the United Nations headquarters as Mr. Ban spoke and Gaza’s main security headquarters, now rubble, ending in front of the Parliament building, also in ruins.

A Hamas spokesman, Ismail Radwan, told the crowd that Israel had not achieved its goals. To several questions, the crowd roared a response. “Have they killed Hamas?” he asked. “No!” “Have they killed the government?” “No!” “Have they dismantled the resistance?” “No!”

He added that Hamas aimed to get Israel to open the border crossings to commercial traffic. “We are aiming for the liberation of all of Palestine,” he said.

The rallies called for international recognition of Hamas as the government here. Most governments in the West and Israel are trying to avoid that prospect.

Tzipi Livni, Israel’s foreign minister, said Israel had achieved its objectives in the war and had sent Hezbollah, the Lebanese militant group, and Iran a message that it would respond if attacked. She opposed any dialogue with Hamas, adding, “It is a terrorist organization.”

The Israeli prime minister, Ehud Olmert, told the visiting Italian foreign minister, Franco Frattini, that Israel would take part in reconstructing Gaza only if Hamas did not lead the process.

In Kuwait, the Arab heads of state condemned Israel’s “barbaric aggression” and demanded an investigation. While urging the reconstruction of Gaza, the group failed to explain how it would carry it out.

The Arab leaders remained divided on how to respond to Israel’s Gaza offensive. Qatar and Syria support Hamas. Egypt, Jordan and Saudi Arabia want to help the Palestinian Authority, which runs the West Bank under President Mahmoud Abbas.

Michael Slackman contributed reporting from Kuwait City, Taghreed El-Khodary from Gaza, and Steven Erlanger from Jerusalem.