US Secretary of State Condoleezza Rice - in Europe to discuss Middle East peace efforts with German and British leaders - said Thursday she heard strong encouragement from Israeli and Palestinian leaders and their neighbors for quick progress toward a peace deal. Rice, scheduled to hold talks with British Prime Minister Tony Blair, earlier briefed Chancellor Angela Merkel in Berlin and said US, German and other diplomats would convene a Mideast strategy session early next month in Washington. As the top US diplomat touched down in winds gusting to 130 km/h in London, Blair faced a political storm as a senior Cabinet minister denounced US President George W. Bush's administration as the most "right-wing in living memory." Peter Hain, Blair's Northern Ireland secretary, said in an interview published Thursday that Bush's "neo-con unilateralism" had damaged the fight against global terrorism and "taken the world's eyes off the ball of solving the Middle East conflict." Hain's office confirmed the comments were accurate. Speaking in Berlin, where she updated Merkel on her Middle East tour, Rice said the US and allies were closely focused on reviving the stalled peace process. "There is no doubt there could be a very important effect on the entire region if we are able to make progress on Middle East peace," Rice said. "I did find the parties very desirous of making progress," she added. "I believe the whole region is looking for ways to make progress and drive toward the establishment of a Palestinian state." She said the Washington meeting next month of the United States, European Union, Russia and the United Nations would come before a US-backed meeting in the Middle East among Rice, Israeli Prime Minister Ehud Olmert and Palestinian Leader Mahmoud Abbas. German Foreign Minister Frank-Walter Steinmeier, who met with Rice on her European tour, said Thursday that a meeting of the so-called Quartet of Mideast negotiators could take place around February 2 in Washington. "Undoubtedly they will reach difficult moments, they will reach times when things are not moving forward," Rice said, stressing that the three-way session does not supplant a dormant 2003 peace plan known as the "road map," although it skips past difficult requirements the plan makes of each side. Rice said in Germany that now is not the time for the United States to talk to adversary Iran, and that the Bush administration is not trying to escalate a confrontation over Iraq. Hain said US policy had damaged, rather than aided, the fight against global terrorism. "It's not only failed to provide a coherent international policy, it's failed wherever it's been tried," Hain was quoted as telling the New Statesman magazine. Blair's Downing Street office declined to comment on Hain's remarks and said talks with Rice would focus on the prospect of bringing Olmert and Abbas together for talks. The British leader made his own visit to the Middle East in December and called for an "early meeting" between Abbas and Olmert. He told reporters Tuesday that Britain, Germany and European allies had a key role to play in bolstering Abbas' authority in his struggle with the Islamic militant group Hamas. "We can play a part in building that capability on the Palestinian side, and the fact is we have got the opportunity in Europe to play a role in this issue in a way that we have not had before," Blair said at a Downing Street news conference. Rice and Blair also were likely to discuss the US plan to increase troop levels in Iraq as Britain prepares to withdraw several thousand soldiers by the end of the year. British Foreign Secretary Margaret Beckett also was to discuss Iran with Rice later Thurday over a private dinner. Last year, the United States said it would join talks with Iran and others if it verifiably halted uranium enrichment, a process that can produce fissile material to fuel nuclear reactors or, at purer concentrations, the core of nuclear weapons.