Bush said: "Am I nudging them forward? Well, my trip was a pretty significant nudge because yesterday they had a meeting."
He said he would step in if and when his involvement is needed.
"You know me well enough to know I'll be more than willing to provide it," Bush said.
Peace groups estimate that there are currently more than 100 "wildcat outposts" in the West Bank - settlements that have not been approved by the Israeli government.
In return, Olmert said 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.
But he said that both sides "are very seriously trying to move forward" on a deal.
Bush said he would press the Palestinians to commit to stopping violence against Israel.
"As to the rockets my first question is going to be to Abbas is what do you intend to do about them," he said.
"There has to be a firm commitment by the Palestinian government to deal with extremists and terrorists who might be willing to use Palestinian territory to launch ... into Israel."
But on the ground, there was no let-up in violence.
The Israeli military fired at Palestinian fighters on Wednesday, killing three people, after a rocket hit a house in the working-class town of Sderot.
For their part, the Palestinian fighters fired at least 13 rockets and mortar shells from Gaza, and at least eight exploded in Israel, police said.
Two struck houses in Sderot, just 1km from the Gaza border fence, a frequent target of the projectiles.
Earlier on Wednesday, Bush arrived in Israel to a warm welcome on his first visit since taking office.
US Air Force One touched down at Ben-Gurion airport outside Tel Aviv, bringing George Bush to Israel before flying by helicopter to West Jerusalem.
Bush, left, is hugged by Peres as Olmert, right,
described the US president as a mentor [AFP]
It is the first visit by a sitting US president in nine years.
In welcome remarks on the tarmac, Shimon Peres, the Israeli president, quickly took the opportunity to warn Iran not to underestimate Israel's resolve to defend itself and thanked the US for its support.
Peres also called on Bush to help "stop the madness" of Iran, Hezbollah and Hamas.
Also greeting Bush was Ehud Olmert, the Israeli prime minister, who said the bond between Israel and the US is "unshakable".
"Your policies have reflected a basic understanding of the challenges facing Israel in this troubled region and a solid commitment to our national security," he said.
In the Gaza Strip, Hamas leaders described the visit as US endorsement of the Israeli occupation while thousands of their supporters took to the streets on Wednesday in protest.
They burned American and Israeli flags and effigies of Bush and Olmert, including a portrait of Bush with the caption "War Criminal Go Home".
Besides Israel, Bush will visit the Palestinian West Bank, Kuwait, Bahrain, United Arab Emirates, Saudi Arabia and Egypt after Egypt.
The Hamas-controlled territory is absent from the tour.
Fawzi Barhoum, a Hamas spokesman, told Al Jazeera: "All the time, the American administration provides all kinds of support to Israel by providing weapons and millions of dollars to support the Israeli occupation, the killings and arrests of the Palestinians as well as the destruction of the Palestinian democratic process.
Barhoum called on Bush to respect the Palestinian democratic process and end Washington's interference.
Speaking to Al Jazeera's David Chater in Ramallah on Wednesday, Khaleel Shaheen, a Palestinian political analyst, said: "For Palestinians the visit will not add anything new. The Americans have red lines that they cannot cross in their relations with Israel.
"This line permits Israel to continue its settlement activities and its aggression against the Palestinians in the West Bank and the Gaza Strip.
"The Palestinians do not expect much from this visit. People here are worried more about the roads that are going to be closed tomorrow rather than worrying about the content of this visit.
"This visit will give a push for both the Israeli prime minister and Palestinian president Mahmoud Abbas. Both leaders are both weak. We should know that Olmert is facing a hard time and needs this visit to strengthen his situation.
"Abbas also needs this visit in order to convince the Palestinians that there is something going on. At least there is contact with the Israelis.
"But we should notice that the Palestinians weakened their position by themselves. They chose to continue these negotiations, while Israel is continuing to build settlements.
"This is something comes in contradiction with the Palestinian stance and against the promise given to Palestinian people that there would be no negotiations as settlement activities going on."
The Israeli view
On the other hand, speaking to Al Jazeera's Jacky Rowland in west Jerusalem, Yossi Beilin, a Knesset member, said: "I do not think that President Bush is coming to solve any problem.
"In my view, I think what he is coming to do is to tell the world and tell us - the Palestinians and Israelis - that he cares, that he believes in the last year of his second term, there is a chance to make peace and to sign a peace treaty.
"This is of some importance after seven years in power, in which he did too little for the peace process in the Middle East.
Bush's challenge is to convince sceptical governments that he is willing to devote the time and effort necessary to bridge decades of differences in the region.
Source: Al Jazeera and agencies