Mr Olmert and Ms Rice met over breakfast at the Prime Minister's private residence in Jerusalem, during which they discussed regional issues - such as Iran's nuclear programme and Israel's peace talks with Syria - in addition to the current conflict in Georgia and its impact on the Middle East.
Mr Olmert told Ms Rice he would make every effort to obtain a written agreement with the Palestinians by the end of the year. During her meetings throughout the day, Ms Rice expressed a keen interest in the ongoing political situation in Israel, particularly the upcoming Kadima party primaries and how the elections will influence the peace negotiations.
Said Mr Olmert's spokesman Mark Regev: "The prime minister reiterated his commitment to continue the work that started at the Annapolis Conference and to continue with the intensive efforts designed to achieve a historic agreement with the Palestinians before the end of the Bush administration."
Ms Rice's visit to Israel on Tuesday was her seventh since talks were re-launched last November in Annapolis, but it was also her shortest. At a press conference with Mr Abbas, Ms Rice said she hoped that an agreement would be reached by the end of Mr Bush's term.
"God willing and with the goodwill and tireless work of the parties, we have a good chance of succeeding," Ms Rice said.
Meanwhile, Defence Minister Ehud Barak flew to Alexandria on Tuesday for talks with Egyptian President Hosni Mubarak as part of Israeli efforts to renew negotiations for the release of captured soldier Gilad Shalit, whose 22nd birthday was marked on Thursday.
Defence officials said that since the ceasefire between Israel and Hamas came into effect in June, Egypt has increased its efforts to stop weapons-smuggling into Gaza. During his meetings, Mr Barak thanked Mr Mubarak for his efforts but urged him to increase them. Israeli security officials recently told the Knesset that tons of explosives as well as dozens of anti-tank missiles have been smuggled into Gaza since the ceasefire began.
Defence officials said following the meeting that despite Mr Mubarak's expressed willingness to increase efforts to secure Corporal Shalit's release, Hamas's recent decision to increase the number of prisoners it demands be released in a swap will prevent renewal of the talks.
