By Sue Pleming WASHINGTON, Nov 27 (Reuters) - Looking to regain diplomatic leadership in the Middle East, the United States said on Monday it saw potential for reviving the Arab-Israeli peace process that many allies consider key to resolving the crisis in Iraq. A weekend cease-fire between Israelis and Palestinians and a "constructive" speech by Israeli Prime Minister Ehud Olmert came just days before President George W. Bush and Secretary of State Condoleezza Rice are set to visit Jordan for talks about Iraq and the Arab-Israeli crisis. Olmert said on Monday Israel was ready to release many jailed Palestinians in return for a soldier seized by militants in June. He also offered to ease travel restrictions on Palestinians and free up frozen funds if violence against Israel ended. "I think this, combined with the announcement of a cease-fire, are certainly welcome developments, certainly potentially promising," said State Department spokesman Sean McCormack. The United States has in recent months been seeking the help of moderate Arab states such as Egypt, Jordan and Saudi Arabia to break the Arab-Israeli deadlock, particularly after the militant group Hamas won Palestinian elections in January. As one way to stop the bloodshed and stem the political crisis in Iraq, those Arab allies, along with European leaders like British Prime Minister Tony Blair, would like Bush to actively try to revive the Middle East peace process. "Our role is to try to help the parties see how they can surmount those obstacles and to bring in neighbors in the region who have an interest in seeing the parties get back to a political horizon," McCormack told Reuters, adding that the United States viewed Olmert's speech as "constructive." Rice is due on Thursday to meet Arab ministers from the Gulf Cooperation Council as well as Jordan and Egypt, on the sidelines of an economic and development conference at a Dead Sea resort in Jordan. OPPORTUNITY? Arab diplomats and U.S. officials said one of the main topics at the Gulf Cooperation Council meeting would be how to push the peace process forward. Iraq and Lebanon are also on the agenda. Asked whether Rice would meet Palestinian President Mahmoud Abbas in Jordan or elsewhere, such as Israel, McCormack left open that she could make other stops or hold other meetings. "We may have additions to the schedule, we'll see. That is always a possibility when the secretary is traveling and especially when she's traveling to the Middle East," he told reporters. Asked whether there were any plans for Olmert to meet Abbas, McCormack said that would be up to the Palestinians and the Israelis to arrange. Washington had hoped the Jordan meeting could provide an opportunity for a broader international peace conference or a meeting between Olmert and Abbas. Another option was for a three-way meeting that included the United States. Last week, hopes for such meetings were not high when Abbas and his Fatah movement, which lost January's elections to Hamas, failed to reach agreement on a new unity government that was more palatable to the West. The United States and many of its allies have imposed a boycott on the Palestinian Authority, blocking funds from directly reaching that authority while Hamas is in control. One Arab diplomat in Washington said the goal was to get the Israelis and the Palestinians to sit down together as soon as possible, but for that to happen prisoners needed to be released on both sides. "They realize that they (the United States) have to deal with the Arab-Israeli conflict but I am not ready to say that this is a new era," the diplomat said. While in Jordan, Rice will also attend Bush's meeting with Iraq's President Nuri al-Maliki.