Nearly a month after the United Nations brokered a cease-fire between Israel and Hezbollah, British Prime Minister Tony Blair offered "sympathy and solidarity" to his Israeli counterpart Saturday for leading his country during difficult times. Blair and Israeli Prime Minister Ehud Olmert held closed-door talks before facing reporters in Jerusalem. Blair planned to visit Lebanon and the Palestinian territory of the West Bank on Sunday. Blair and Olmert restated their commitment to advancing the political process to secure a Middle East peace, with Olmert offering to meet with Palestinian President Mahmoud Abbas -- without conditions -- but with the goal of obtaining the release of two Israeli soldiers in Hezbollah custody, the Associated Press reported. Blair described the 34-day battle between Israel and Hezbollah as "a terrible situation during which many people have suffered," and expressed sympathy for everyone who suffered losses. If U.N. Resolution 1701 is implemented, he said, referring to the resolution that on August 14 ended the 34 days of fighting, "this will be a major strategic advance for peace in the region." "The stability of this region now affects the stability of my country" and throughout the world, Blair said. Olmert said he wants to get the Middle East peace process back on track using the "road map," the international peace plan that was introduced in 2003.