WASHINGTON, Sept 6 (Reuters) - The U.S. commander in Iraq, Gen. David Petraeus, has told President George W. Bush he wants to maintain heightened troop levels in Iraq well into next year but could accept the pullback of about 4,000 troops beginning in January, The New York Times reported on Thursday.

Petraeus wants to reduce the risk of military setbacks but his recommendation could also satisfy some critics in Congress, the newspaper said, citing senior administration and military officials.

Petraeus "is worried about risk, and all things being equal he'd like to keep as much as he could for as long as he could," a senior military officer told the Times.

In congressional testimony next week, Petraeus will discuss the possibility of far deeper withdrawals, over a period of months beyond January, that could bring levels down to about 130,000 troops, the newspaper reported, citing officials helping prepare the testimony.

The officials, who were not named, told the Times it was not clear how specific Petraeus would be in discussing the timing of pullbacks in the public setting.

Several officials involved in internal discussions about the testimony said that both Petraeus and Lt. Gen. Raymond Odierno, the ground commander in Iraq, were worried about signing on to a timetable that would commit them to steep withdrawals in the spring, newspaper said.

Asked about the report, White House spokesman Gordon Johndroe, who was traveling with Bush at an Asia-Pacific summit in Australia, said: "Gen. Petraeus will testify before Congress next week. We should wait to hear from him then. Any decisions made will be based on conditions on the ground."

The U.S. Congress must decide in coming weeks whether to approve more funding for the war, and Democratic leaders are seizing on the reports as evidence that Washington should start bringing home some of its 168,000 U.S. troops in Iraq.

A small but growing number of Republicans have also expressed doubts about the U.S. strategy on the unpopular war.

The White House will submit its own assessment by Sept. 15, after testimony by Petraeus and Ryan Crocker, the U.S. ambassador to Iraq, report to Congress. That report is expected to provide Bush with a blueprint for his administration's next move in Iraq.

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