Mr. Bush and Palestinian leader Mahmoud Abbas spoke to reporters Thursday after what Mr. Bush called "good talks" at the White House.
Both leaders described Israel's recent withdrawal from the Gaza Strip as an opportunity, and hailed the coming Palestinian parliamentary elections as a step forward for democracy.
Mr. Bush said the next step was to confront what he called "armed gangs" he said threaten the elections and the prospects for lasting Israeli-Palestinian peace.
He also said Israel must stop settlement activity in the West Bank, and said it is important that the sides make progress on opening crossings to Gaza.
Mr. Abbas said Palestinians are committed to reaching a negotiated settlement with Israel, but he said the time has come to move quickly toward permanent status talks.
This is the first time Mr. Bush and Mr. Abbas have met since Israel ended its 38-year occupation of Gaza last month.