US President George W. Bush and Prime Minister Ehud Olmert praised each other's visions for peace between Israelis and Palestinians Monday as each leader prepares to leave office without seeing that dream fulfilled. "We strongly believe that Israel will benefit by having a Palestinian state, a democracy on her border that works for peace. And, Prime Minister, that vision is alive because of you. And I thank you for your steadfast support for peace," Bush told Olmert ahead of a meeting in the Oval Office Monday night, which was followed by a private dinner. In return, Olmert mentioned the Annapolis negotiating process, which Bush initiated a year ago, and stressed his commitment to it for as long as he remains in office. "It continues with your guidance, support and inspiration. And this is very important, because as you say, a two-state solution is the only possible way to resolve the conflict in the Middle East," Olmert said. A major goal of the farewell visit has been to secure continuity of the negotiating process for the next administration. Bush's term ends in January and Olmert will be departing following the elections in February. The two lame-duck and unpopular leaders also exchanged words of praise, with Bush telling Olmert, who was forced to step down because of his part in an unfolding corruption scandal, that when it came to the peace process, "One thing is for certain - you've kept your word. And in international politics, that's important." Olmert, in return, praised Bush for his strong concern for Israel's security and for removing Iraqi leader and Israel's foe Saddam Hussein from its eastern front. Though many have objected to Bush's decision to embark on the Iraq war, and Olmert has come under criticism from American Jewish groups for praising the politically sensitive effort, he remarked at Monday's photo op, "I will never forget that you have removed one of the most threatening strategic dangers from Israel on the east side, in Iraq. And this is a great achievement that makes life much better for many people in our part of the world." Their meeting had been expected to focus on Iran, Syria and the peace process, the latter of which was a central topic of conversations Olmert held earlier in the day with US Secretary of State Condoleezza Rice, with whom he will meet again on Tuesday morning. "It was agreed that the Annapolis framework would continue after the existing administrations," said an Israeli diplomatic official familiar with the morning meeting. Even so, he said that there was currently no plan for a written document to be created detailing the progress and positions of both sides, but rather for the status of the talks to be transmitted verbally. Despite American interest in a document, both Israelis and Palestinians have opposed codifying the agreements reached so far, which have so far been shrouded in secrecy. There is some concern that leaks could torpedo the efforts if not part of a comprehensive effort unveiled to the respective publics simultaneously. Any compromises would also be politically sensitive and could affect the elections in Israel and the leadership struggle within the Palestinian Authority, as Abbas is also slated to come to the end of his term in office. Also in the meeting, which included US National Security Advisor Stephen Hadley, Olmert expressed concerns about Western elements reaching out to Hamas. Olmert stressed the importance of shunning Hamas until it meets the international Quartet's demands of renouncing violence and recognizing Israel. His comments at the closed-door meeting come as European parliamentarians this month invited Palestinian legislators, including Hamas representatives, to visit Brussels. Several European lawmakers have also been among those ferrying humanitarian supplies and transferring Palestinians to Gaza in defiance of an Israeli blockade. At the same time, questions about America's commitment to the nearly three-year-old policy, which has been criticized by some international leaders since Palestinians elected Hamas in 2005, have been raised anew with the change in US leadership in January. Hamas has suggested that with the new Obama administration, there could be an opportunity for dialogue, and there had been reports that Obama campaign advisers had met with Hamas. One adviser left the campaign once these reports surfaced and the campaign strongly denied other contacts. Obama himself has stressed repeatedly that he would not meet with Hamas so long as the Islamic extremist group doesn't adhere to the Quartet's conditions. Olmert has no planned meetings or phone calls with Obama, according to the Israeli embassy, though he did meet with one of his earliest Congressional backers, Florida Rep. Robert Wexler, later Monday morning.