President George W Bush will this week announce he plans to reduce US troops in Iraq by about 30,000 by next summer, White House officials say.
Mr Bush (right) will endorse Gen Petraeus' proposals, officials say
They say the cuts, with conditions attached, will be announced by the president in a major TV address.
The move would bring the number of US troops in Iraq to "pre-surge" levels.
The US top military commander in Iraq and the US envoy in Baghdad have told Congress that the surge, launched in February, is working.
President Bush will make the speech on Thursday night at 2100 local time (0100GMT on Friday).
The White House says it will contain an endorsement of the troop reduction proposed by Gen David Petraeus, who has been testifying in Congress on Monday and Tuesday.
However, Mr Bush is expected to condition his plans - and also further troop cuts - on continued progress in Iraq.
The BBC's Justin Webb, in Washington, says the president's move is an attempt to seize the initiative and to give the impression - whether true or not - that he is driving events.
Gen Petraeus - and also US envoy in Iraq Ryan Crocker - faced severe criticism during the two days of their testimony in Congress from lawmakers opposed to the war.
Sen Joseph Biden (D) - who chairs the Foreign Relations Committee - said on Tuesday that the surge had failed to promote reconciliation between Sunnis and Shia, and was at best "a stopgap that will not prevent chaos".
House of Representatives Speaker Nancy Pelosi (D) said: "It sounds to me as if Gen Petraeus is presenting a plan for at least a 10-year, high-level US presence in Iraq."
Gen Petraeus said that violence in Iraq had declined significantly since February, but stressed that a premature troop reduction would have "devastating consequences".
A record 168,000 US troops are now in Iraq after 30,000 arrived in the surge between February and June.