(Adds State Department comments) By Adam Entous JERUSALEM, June 25 (Reuters) - Tony Blair is likely to be named as early as Tuesday to a top post in Middle East peacemaking to try to bolster prospects for a Palestinian state despite Hamas's takeover of the Gaza Strip, diplomats said. Blair steps down as British prime minister on Wednesday and officials are working to define the role he would play as envoy for the Quartet of international peace brokers -- the United States, the European Union, the United Nations and Russia. Blair's appointment is expected to top the agenda in talks on Tuesday in Jerusalem between officials representing U.S. Secretary of State Condoleezza Rice, U.N. Secretary-General Ban Ki-moon, EU foreign policy chief Javier Solana and Russian Foreign Minister Sergei Lavrov. Washington confirmed that the Quartet was discussing the appointment of an envoy to help Palestinian President Mahmoud Abbas build up the institutions of a future Palestinian state and carry out political and economic reforms. "In terms of the who or greater details ... we'll let the Quartet get together and make those determinations," deputy U.S. State Department spokesman Tom Casey said. Sources familiar with the Quartet's deliberations said an announcement on Tuesday was likely, although one source said Blair may not start work immediately. "There are consultations going on between members of the Quartet and the UK about appointing Tony Blair as Quartet envoy to the Palestinians," a European diplomat said. "I cannot say whether there is a result, but I expect a result possibly on Tuesday when the Quartet envoys meet, perhaps even sooner." Blair, a close ally of U.S. President George W. Bush, has frequently urged Washington to take a more assertive role in the Middle East but has not said definitively whether he wants the envoy job. Diplomats close to the negotiations said Blair, who steps down after 10 years in power, appeared ready to take the job and to have overcome some resistance within the Quartet. Negotiators were now trying to iron out details about the envoy's mandate. Some in Russia and Europe have questioned his ability to win Arab support after taking a leading role in the Iraq war with Bush. Many Arabs believe Bush is biased in Israel's favour. SCHISM An official for the Islamist Hamas group said that "the experience of our people with Blair was bad". His appointment as Quartet envoy "may even make things worse", the official, Sami Abu Zuhri, said. The Bush administration first floated the idea of appointing Blair as Quartet envoy earlier this year, long before Hamas Islamists seized control of the Gaza Strip more than a week ago. Abbas responded to Gaza's takeover by sacking the Hamas-led government and forming an emergency cabinet in the West Bank. That has divided the Palestinian territories into two separate fiefdoms -- a Hamas-controlled Gaza and a larger, Fatah-dominated West Bank. As part of a strategy to counter Hamas, Israel and the United States want to isolate the Islamists in the Gaza Strip, while bolstering the emergency government set up by Abbas. The Bush administration hopes to spur negotiations between Abbas and Israeli Prime Minister Ehud Olmert, who met in Egypt on Monday, as well as promote an Arab land-for-peace initiative. Olmert supports Blair taking on an expanded role in the region after he steps down as prime minister, aides said. The Quartet's previous envoy, former World Bank president James Wolfensohn, focused largely on economic issues. He resigned in frustration, in large part over Israel's unwillingness to comply with U.S.-brokered agreements. (Additional reporting by Paul Taylor in Brussels and Sophie Walker in London)