But the prospect of reaching a peace deal during Bush's term, which ends in January 2009, have evaporated in recent months.
Discussions 'to continue'
"It's important that we maintain momentum for the negotiations," Perino said.
"Over the past year, we have laid some very good ground work for the Palestinians and the Israelis to be able to continue to have their discussions."
For their part, Palestinian and Israeli leaders have said in recent weeks that a peace deal will not be reached by the end of the year.
Earlier on Thursday, Condoleezza Rice, the US secretary of state, said there was little prospect of Israel and the Palestinians reaching a deal this year.
Speaking at the beginning of a four-day trip to the Middle East, Rice said Israel's decision to hold a parliamentary election, scheduled for February 10, was an obstacle to further negotiations between Israel and the Palestinian government.
Rice is set to meet Olmert, who has announced plans to resign because of a corruption scandal, and the three people who are looking to succeed him.
Tzipi Livni, Israel’s foreign minister and the leader of the ruling Kadima party, was seen as the inheritor of the premiership from Olmert, but last week she called for a general election after failing to form a coalition government.
She will face her stiffest challenge from Benjamin Netanyahu of the Likud party, who is criticial of the peace process, and Ehud Barak of the Labor party.
The peace talks had also been stymied by the continuation of Israel settlement construction, which is illegal under international law, and violence in and around the Gaza Strip.
The coastal territory is under the de facto control of Hamas, which routed Fatah loyalists in June 2007. Israel and the US brands Hamas a terrorist organisation.