JERUSALEM (CNN) -- President Bush claimed credit Wednesday for "nudging" Israeli and Palestinian leaders toward a two-state peace deal just hours after he arrived in the region on a Mideast tour.
Bush joined Israeli Prime Minister Ehud Olmert at a news conference on Wednesday after meeting in Jerusalem.
Bush, after more than two hours of talks with Israeli Prime Minister Ehud Olmert, said he was pleased to watch Israeli and Palestinian leaders work hard to try to achieve the vision of peace in the region.
"The only way to have lasting peace ... is for the two parties to come together to make the difficult choices, but we'll help," said Bush during a news conference at the prime minister's residence.
"If you're asking me, 'am I nudging them forward,' well, my trip was a pretty significant nudge because yesterday, they had a meeting," said Bush.
Bush took credit for Tuesday's meeting between Palestinian Authority President Mahmoud Abbas and Olmert, which Israel said resulted in an agreement to have both sides "conduct direct and ongoing negotiations on all final status/core issues."
On Thursday, Bush is scheduled to travel to the West Bank to meet with Abbas.
But the difficult road to peace was highlighted by Israeli reports Wednesday of short-range Qassam rocket attacks on Israeli homes from Hamas-controlled Gaza. Israel responded with ground and airstrikes into northern Gaza.
"As long as there is terror from Gaza, it will be very, very hard to reach any peaceful understanding between us and the Palestinians," said the Israeli prime minister.
Olmert said Palestinian leaders "understand that Gaza must be a part of the package."
A top U.S. adviser said the attacks were a major concern for Israelis as they were about to enter the peace talks.
The U.S. president drew a picture of an independent Palestinian state as an alternative to Palestinians led by Hamas, an Islamic fundamentalist group listed by Washington as a terrorist organization and which refuses to acknowledge Israel.
"Here's your choice: You can have the vision of Hamas, which is dangerous and will lead to war and violence, or you can have the vision of a state, which should be hopeful," said Bush.
Bush also used the news conference to criticize Iran, days after a confrontation between U.S. Navy and Iranian vessels in the Persian Gulf. "The United States, Bush said, "will continue to work with European countries and Russia and China as well as nations in this neighborhood to make it abundantly clear that the threat that Iran poses to world peace."
Calling his mission a "historic moment, historic opportunity," Bush met with Olmert after arriving in Israel on the first leg of a tour aimed at jump-starting the Israeli-Palestinian peace process and meeting with leaders of Arab nations.
"Arab leaders have an obligation to recognize Israel's important contribution to peace and stability in the Middle East, and to encourage and support the Palestinians as they make tough choices," Bush said.
Earlier Wednesday, Bush met with Israeli President Shimon Peres, saying he came away "with high hopes."
Peres told Bush "The process may be slow, but the progress can be sweet."
Watch more on Bush's arrival »
En route to the talks, national security adviser Stephen Hadley expressed concern to reporters aboard Air Force One about "distractions" to the peace process. "The Palestinians are very concerned, obviously, about settlements; the Israelis are very concerned, obviously, about the rocket attacks coming out of Gaza. These issues need to be addressed," said Hadley. Watch how Israeli settlers reject proposed freeze »
Bush will "encourage the parties to get after it, to stay focused," said Hadley.
The president "will hear from the parties on where their negotiations and their discussions are," he said. "And I think he will say some words that are encouraging to the process, but I don't think you're going to see him jumping into the middle of these negotiations."
Security was tight for Bush's visit to the region. Large parts of Jerusalem as well as much of the West Bank, including Ramallah, will be, in effect, shut down.
More than 10,000 police will be deployed across the region to back U.S. federal officers in what is the largest security operation in Israel since Pope John Paul II's visit in March 2000.
Security will also be heavy at a number of large demonstrations in Israel planned to protest Bush's visit.
To minimize his exposure, Bush will do most of his traveling by helicopter, but some stops on in his itinerary, particularly in the West Bank, are reachable only by car and on foot. That, security analysts say, will be the most dangerous time for the president.
During his tour of the West Bank, the Palestinian Authority will aid U.S. security teams in protecting the president.
Bush is scheduled to depart Jerusalem on Friday for Kuwait. He will then head to Bahrain, the United Arab Emirates, Saudi Arabia and Egypt. He returns to Washington next Wednesday.
A major challenge for Bush will be keeping the trip focused on Israeli-Palestinian peace while other issues -- Iran, Pakistan, Iraq and soaring oil prices -- dominate the media headlines and serve as reminders of the region's instability.
Bush hopes to have a peace deal before he leaves office in a year, and both Abbas and Olmert agreed to work toward such an agreement at the November 27 U.S.-sponsored peace summit in Annapolis, Maryland.
Subsequent meetings between the Israeli and Palestinian delegations have been overshadowed by disagreements over Israel's plans to expand settlements in disputed areas of the West Bank. E-mail to a friend 
CNN's Ed Henry and Atika Shubert contributed to this report.
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