Washington, D.C. ? President George W. Bush and Israeli Prime Minister Ehud Olmert bid each other farewell on Monday, expressing confidence in an eventual Mideast peace deal that won’t materialize on either of their watches.

Bush and Olmert met for more than an hour at the White House as their time in office winds to a close. Bush’s two terms end Jan. 20. Olmert plans to resign amid corruption charges and will step down after a successor is chosen on Feb. 10.

Bush, speaking to reporters before their talks in the Oval Office, said Olmert kept his word — “and in international politics, that’s important.”

“We’ve been through a lot together during our time in office,” Bush said. “We strongly believe that Israel will benefit by having a Palestinian state, a democracy on her border that works for peace. … It’s not easy to try to change the paradigm, and I understand that.”

Olmert said history will owe Bush a debt of gratitude for setting the region on the path to an accord.

“A two-state solution is the only possible way to resolve the conflict in the Middle East,” Olmert said.