Support forces are in addition to the 21,000 troops announced by Obama, US daily says.
But the US president has said that the main focus on any new policy would stick to the US’s current aim to defeat al-Qaeda and its “extremist allies” – a reference to Taliban fighters.
“We are going through a very deliberative process,” Obama said on Tuesday after talks with Jose Luis Rodriguez Zapatero, Spain’s prime minister.
“I won’t provide you a preview of what I am seeing or hearing … I would expect that we will have a completion of this current process in the coming weeks,” he said.
“There are many pieces that all have to fit together – militarily, civilian, diplomatically – all of which have to work together to ensure a policy that works for our allies and for our goal of destroying al-Qaeda”
Robert Gibbs, White House spokesman
The reported request by McChrystal for thousands of extra US troops to Afghanistan comes as the US military enters the ninth year of its fight against al-Qaeda and Taliaban fighters.
This year has proven to the deadliest so far for US and Nato troops serving in Afghanistan, with at least 409 soldiers and military personnel killed, according to icasualties.org.
US public support for the war in Afghanistan has fallen in recent months, while several senior Democrats have said that expanding the size of the US force in the country runs the risk of it being seen as an occupying force by the Afghan population.
The number of US troopps in Afghanistan is already scheduled to hit 68,000 by the end of the year, in line with a previous order by Obama.
But McChrystal has warned that the mission in Afghanistan risks failure unless a further boost in troops number is authorised by the US president.
While Obama has made no commitment of US military strategy, the White House has said that there will no large-scale withdrawal of troops.
“We need a policy that works. And if that takes a little bit more time to get right, I think that’s what the American people expect,” Robert Gibbs, the White House spokesman, said.
“There are many pieces that all have to fit together – as I said, militarily, civilian, diplomatically – all of which have to work together to ensure a policy that works for our allies and for our goal of destroying al-Qaeda.”
The White House appears to be suggesting that the main focus in the war in Afghanistan is to defeat al-Qaeda fighters, who are considered to constitute a larger threat to the US and its interests than the Taliban.