The Times had reported some aides telling Bush it would be wiser to announce his intention of a troop pullout if he wanted to forestall more defections.
But Tony Snow, the White House spokesman, said there was "no debate right now" on troop withdrawal and that the idea of a political judgment on it, instead of a military one, is "simply not true".
"The president has said many times, that as conditions required and merit, that there will be, in fact, withdrawals and also a pulling back from areas of Baghdad and so on," he said.
Shoring up support
"A growing number of Republicans are now speaking against the failed strategy in Iraq, and that's good"
Harry Reid, Senate Majority Leader
The president had originally rejected this strategy in December when it was proposed by the bipartisan Iraq Study Group.
The issue will be addressed later this week when the mid-July interim assessment of progress in Iraq is released, and not when the full report is due in September.
An official told The Associated Press that the facts were not in question but rather "how the White House proceeds with a post-surge strategy in light of the report".
A draft version of the progress report was circulated among various government agencies in Washington on Monday.
Harry Reid, the senate majority leader, said the coming weeks would reveal whether the Republicans opposed to the present course of action in Iraq would be willing to vote for a troop withdrawal.
"A growing number of Republicans are now speaking against the failed strategy in Iraq, and that's good."
Reid added the senate debate on Iraq, with voting expected on Tuesday, would be part of work on a defence policy bill.
Key Republicans pleaded for more time suggesting that voting be held back until Bush reports on the progress in Iraq on September 15, a requirement of a recent war funding bill.
Meanwhile, a US general warned that the fight against the Iraq uprising was "a long-term endeavour" that could take decades.
General David Petraeus, the top US commander in Iraq, cited the case of Northern Ireland and Britain to show that reconciliation may happen after a very long time.
"Anybody... would recognise that these are long-term endeavours," Petraeus told the BBC from Baquba, northeast of the capital.
He said the recent surge of 30,000 US troops was having a positive effect in some parts of the country including the capital, Baghdad.
He said the more important question is how many US soldiers would still be needed in Iraq and how "can we gradually reduce our forces so we reduce the strain on the army, on the nation".
Added Petraeus: "We do believe that this is achieving progress. The bigger issue of course is whether we can then also get the grassroots reconciliation going, and that actually is working."