But Gates will hang onto the request until the White House and Pentagon get to a "proper stage" in their assessment of the war in Afghanistan, Pentagon spokesman Geoff Morrell said, explaining that it is premature for the request to be considered until the assessment is fully reviewed.
Sources have told FOX News that Gen. Stanley McChrystal wants 30,000 to 40,000 additional troops.
An array of powerful lawmakers from both parties, including the Democratic chairman of the House Armed Services Committee, want McChrystal to testify about the challenges confronting the U.S. and its allies in Afghanistan and his plan for beating back the resurgent Taliban.
But the Pentagon is rebuffing those calls, amid the growing political tumult over the Obama administration's handling of the conflict.
Democrats and Republicans in Congress note that the Bush administration made Gen. David Petraeus, the former top U.S. commander in Baghdad, available for days of high-profile hearings on the conduct of the war in 2007, as a similar debate was raging over troop levels in that war.
"You hear it from the horse's mouth," said Rep. Ike Skelton, D-Mo., the chairman of the House Armed Services Committee. "He is the general in charge."
House Majority Leader Steny Hoyer, D-Md., echoed the call for Gen. McChrystal to testify, telling reporters that it "would be useful" for the commander to personally tell lawmakers about "his sense of the success that changing strategies would have."
Gates has refused to make McChrystal available for testimony on Capitol Hill until the administration completes a broad review of its entire strategy for the war. "Secretary Gates still believes Gen. McChrystal's focus right now should be on managing the war in Afghanistan rather than wading into the debate about it back here in Washington," Pentagon spokesman Geoff Morrell said.
The Obama administration announced a new counterinsurgency strategy for Afghanistan in March that was designed to protect Afghan civilians from violence, and to improve their daily lives through economic development and better governance.
Some administration officials now believe that approach should be discarded in favor of a stepped-up push to kill individual Taliban leaders and financiers -- a strategy long favored by Vice President Joe Biden.
Morrell acknowledged that additional inputs and strategies are being discussed at the White Houe but he would not shed any light on what they are.
FOX News' Jennifer Griffin and Justin Fishel contributed to this report.