Palestinian rockets were fired into Israeil, while an Israeli air strike killed three Palestinians in Gaza.
'Outposts ought to go'
"I'm under no illusions," Bush said at a joint news conference with Olmert in Jerusalem on Wednesday. "It's going to be hard work."
Calling it "an historic moment and opportunity" for peace, Bush said Israel should remove Jewish settlements built without government authorisation in the occupied West Bank.
"Outposts, yeah, they ought to go," Bush said.
Olmert has pledged to remove them but has not given a deadline.
Bush said he believed both Olmert and Abbas were 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," Bush said.
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.
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, 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 Bush to Israel before flying by helicopter to West Jerusalem.
|Olmert, left, said said the bond between Israel|
and the US is "unshakable" [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 Olmert, who said the bond between Israel and the US is "unshakable".