JERUSALEM — President Bush, in the Middle East to push along a peace deal by the end of his presidency, gave orders to both sides today. He told Israelis that “illegal” settlement outposts in disputed land must go and told Palestinian Arabs that no part of their territories can be “a safe haven for terrorists.”

On that, Mr. Bush was echoing his ally and host, Prime Minister Olmert, who said in their joint news conference that “there will be no peace” unless attacks are halted from all parts of the Palestinian Arab territories, including those not controlled by his negotiating partners in the Palestinian Arab leadership. Mr. 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,” Mr. Olmert said, after two and a half hours of talks with Mr. 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.”

Today, Israeli strikes in the Gaza Strip killed one militant and two civilians, according to Palestinian Arab medics. The Israeli army said the attacks were needed because Palestinian Arab 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 Middle East trip aimed at encouraging a long-elusive Israeli-Palestinian Arab agreement, Mr. Bush declared there is a “historic moment, a historic opportunity.” He added, “I’m under no illusions. This is going to be hard work.”

Mr. Bush said he and Mr. 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. American 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.

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

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

Clearing up confusion about American policy toward Iran is a key subtext of Mr. Bush’s trip, which will also take him to Kuwait, Bahrain, United Arab Emirates, Saudi Arabia, and Egypt. Mr. Bush visits the Palestinian Authority president, Mahmoud Abbas, tomorrow in the West Bank, a Palestinian Arab territory. But he will not stop in or near the Gaza Strip, the other Palestinian Arab territory which is controlled by Islamic Hamas militants who are not a party to negotiations. It was from Gaza that militants launched rockets today into southern Israel and where Palestinian Arab 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 Arab state can be created. “At this point, it’s a pretty depressing situation,” Mr. Hadley said of the split in Palestinian Arab control.

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

But Mr. 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.

Mr. Bush said he believes both Messrs. 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 Mr. Bush’s arrival, Messrs. 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 Arab refugees, and Israeli security concerns.

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

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

Mr. Bush didn’t go as far as Ms. 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.”

Mr. OImert said Israel “must abide by our commitments and we shall do so.”

An adviser to Mr. Abbas, Nabil Amr, said Mr. 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.

Mr. Amr said America 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.

Mr. Bush also indicated a willingness to address Israel’s concerns with the Palestinian Arabs.

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,” Mr. Bush said.

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

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

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

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

Mr. Bush’s first formal meeting was with President Shimon Peres, at his official residence. Mr. Peres said the Annapolis conference started a one-year clock on the difficult Middle East peace process, underscoring Mr. Bush’s hopes — considered unrealistic by many in the Middle East and America — to conclude a deal before he leaves office. “Time is so precious,” Mr. Peres said.