(Updates with Bush TV interview paragraphs 5-7, 16) By Tabassum Zakaria WASHINGTON, Oct 16 (Reuters) - U.S. President George W. Bush assured Iraqi Prime Minister Nuri al-Maliki on Monday that the United States had not set any deadline for his government to control sectarian violence and still supported his leadership, the White House said. Maliki raised concerns about a timeline, saying such rumors undermined confidence in the Iraqi government and inspired terrorists, during a 15-minute telephone call initiated by Bush, White House spokesman Tony Snow said. "The president underscored his commitment to a democratically elected government of Iraq, encouraging the prime minister to ignore rumors that the United States government was seeking to impose a timeline on the Maliki government," Snow said. The Iraq war, in which about 2,750 American troops and tens of thousands of Iraqis have been killed, has dragged down Bush's popularity before elections in which his Republican Party is fighting to keep control of Congress. Bush has insisted that U.S. troops will not withdraw until Iraqis are able to take over security. "Ultimately, a success in Iraq is going to depend upon the Iraqi people's willingness to do the hard work," Bush said in an interview with Fox News Channel's "The O'Reilly Factor." Bush said creating three autonomous regions in Iraq was not the answer and would only create "a bigger mess than we have at this point in time, which I believe is going to be solved." In the weeks before Nov. 7 congressional elections, some top Republicans began to express dissatisfaction with the direction in Iraq, where sectarian violence has raised fears that the country is sinking into an all-out civil war. Senate Armed Services Committee Chairman John Warner, a Virginia Republican, has said the United States might have to consider a change of course if the Iraqi government fails to restore order within two or three months. Another senior Republican, Sen. Chuck Hagel of Nebraska, on Sunday said he agreed with Warner's assessment. "Our options are limited. The American people are not going to continue to support, sustain a policy that puts American troops in the middle of a civil war," Hagel said on CNN's "Late Edition." Democrats, who have long called for a change of direction in Iraq, have stepped up criticism of the Bush administration's conduct of the war in the last stretch before the elections. RUMORS Maliki was concerned about rumors there would be an effort to replace him if more progress was not made, and Bush said: "The rumors are not true, we support you," according to Snow. While Bush expressed confidence in Maliki, "there is more to be done," Snow said. "The violence level's absolutely unacceptable. And it is important to make progress." The bloodshed in Iraq showed no sign of letting up, with car bombs killing at least 30 people on Monday. Bush supports Maliki's efforts to go after militias and terrorists through political, economic and military means, Snow said. The United States was concerned about some Iranian involvement in the Iraq insurgency, but the instability was a mixture of sectarian, criminal and al Qaeda violence, Bush said. "And so obviously, if we see more Iranian involvement, we'll adjust our tactics to meet that threat," he said. The White House will look seriously at recommendations on Iraq expected after the election from a panel co-chaired by James Baker, a former Secretary of State with ties to the Bush family, Snow said. "But we're not going to outsource the business of handling the war in Iraq."