US President George W. Bush said that he and Iraqi Prime Minister Nouri al-Maliki agreed in high-stakes talks Thursday that Iraq should not be partitioned into separate, semi-autonomous zones. "The prime minster made clear that splitting his coutnry into parts, as some have suggested is not what the Iraqi people want, and that any partition of Iraq would only lead to an increase in sectarian violence," Bush said after nearly two and a half hours aimed at stabilizing violence-wracked Iraq. `I agree," he said. Bush and al-Maliki on Thursday opened talks originally set for the day before but canceled following disclosure of US doubts about the Iraqi leader's capabilities and a Baghdad protest of his attendance. Instead of talks over two days, the stunning turn of events found Bush and al-Maliki meeting for a working breakfast that was to be followed by a longer session and a news conference. The Iraqi prime minister came to Bush's hotel. Bush had jetted into Amman Wednesday night to hold crisis talks with al-Maliki. The delay was announced shortly after Bush arrived for talks hosted by King Abdullah II, whom he met as scheduled. White House counselor Dan Bartlett denied the move was a snub by Maliki or was related to the leak of a White House memo questioning the prime minister's ability to control violence in Iraq. "Absolutely not," Bartlett said. "He said the king and the prime minister had met before Bush arrived from a NATO summit in Latvia. It negated the purpose for a meeting of the three of them." Bush and Maliki are under growing pressure to prevent sectarian violence in Iraq from turning into civil war. Critics on both sides have questioned their ability to stabilize the country. In protest against the Bush-Maliki meeting, the powerful Shi'ite cleric, Muqtada al-Sadr, withdrew his faction from the fragile Baghdad government. His support had helped make Maliki prime minister. Bush has blamed al-Qaida for the current violence and has vowed not to pull the 140,000 US troops out of Iraq "before the mission is complete." On Tuesday, the UN Security Council voted unanimously to renew the US-led coalition's mandate for another year. But this hasn't allayed regional concerns about what would happen should a premature withdrawal take place. Israelis worry such a move would create a vacuum that Iran and al- Qaida would fill. Jordanians fear it could destabilize their country from the east. "Ultimately the US needs to get out of Iraq, but it can't happen prematurely," a Jordanian analyst told The Jerusalem Post. "A premature withdrawal will result in a security vacuum that will affect the whole region and result in further violence. The repercussions for Jordan would be enormous, both in terms of security threats and demographics. The American military presence is essential for now, but ultimately what we need is a US road map for withdrawal. The Iraqi police and army need to be equipped for this." To that end, Jordanian King Abdullah initiated this week's round of meetings focusing primarily on Iraq, the Israeli-Palestinian conflict, and, at the request of Lebanese prime minister, continuing Israeli infringements of Lebanese sovereignty. "The situation with Iraq is very grave. It's a vicious circle. If the foreign forces leave, the violence will worsen, but if there is not a visible exit strategy and timetable, then the situation will still get worse," another Jordanian analyst told the Post. "It's very difficult to offer simple solutions to such a complex problem. The security situation is not stabilizing; it is going from bad to worse," the analyst said. One by-products of the growing violence is an increase in the number of Iraqi refugees fleeing to Jordan. According to Human Rights Watch, nearly a million have already entered the country. An estimated 1,000 arrive each day. There are also fears here of a possible massive influx of Palestinian refugees as a result of an Israeli-Palestinian peace deal. Addressing his parliament on Tuesday, King Abdullah said resolution of the Israeli-Palestinian conflict was central to stability in the region. He is expected to devote a large part of his talks with Bush to the issue. Abdullah has made it clear he opposes any deal that "discriminates against the Palestinians" or that comes at Jordan's expense. "Jordan is not a rich country. We have a poverty rate of 30 percent, and yet we have opened our doors to a huge numbers of Iraqis," the local analyst said. "Fortunately, I don't foresee an influx of Palestinian refugees like before. Palestinians don't want to leave their homes like they did in '48 and '67. By now they're used to the hardships of occupation. But certainly economic pressures could push people away in search of better living conditions," he said. Not many are hopeful this week's deliberations will offer up any new answers. US Secretary of State Condoleezza Rice is accompanying Bush and is expected to meet with Palestinian Authority Chairman Mahmoud Abbas in Jericho on Thursday. She will also meet with Prime Minister Ehud Olmert in Israel the same day. Saturday's Gaza cease-fire announcement did lead to some cautious optimism in Washington but there is no sense of dramatic momentum leading to a renewed Israeli-Palestinian diplomatic process. In Amman, hundreds staged sit-ins and shouted fiery anti-Bush slogans at several demonstrations scattered throughout the capital. Security was beefed-up, with bomb-sniffing dogs at hotels and tanks and troops dotting the main highway from the airport to downtown. At one street demonstration, about 1,000 people from several opposition groups and political associations marched to the Prime Ministry building where they burned American and Israeli flags and an effigy of Bush. Many carried portraits of ousted Iraqi leader Saddam Hussein. At another rally, organized by Jordan's branch of the Muslim Brotherhood, about 300 people carrying Jordanian flags and anti-Bush banners marched through the University of Jordan. One demonstrator held a sign that read: "You are not welcome in Jordan. You have our children's blood in your hands," while another banner said: "Bad Bush, you are not welcome in our homeland Jordan." Overall, the protests were smaller than expected and no clashes were reported, though security was tight. Several Jordanian newspaper columnists expressed doubt that the Bush-Maliki talks would offer any breakthroughs on Iraq and the other political hotbeds - Lebanon and the Israeli-Palestinian crisis. "Many believe that sectarian violence [in Iraq] has gone well past the point of no return," columnist Hasan Abu Nimah wrote in The Jordan Times. "There are no quick solutions for either Palestine or Iraq. The situation in Lebanon, Syria and the rest of the Arab world is directly linked to both crisis areas. That simply means matters on both fronts are bound to get worse and the American entanglement in Iraq will deepen, too," he said. AP contributed to this report.