The Pentagon is rebuffing congressional calls for the top U.S. commander in Afghanistan to personally make the case for the war, amid the growing political tumult over the Obama administration's handling of the conflict.

An array of powerful lawmakers from both parties, including the Democratic chairman of the House Armed Services Committee, want Gen. Stanley McChrystal to testify about the challenges confronting the U.S. and its allies in Afghanistan and his plan for beating back the resurgent Taliban.

The calls to testify come as the Pentagon has asked Gen. McChrystal to delay his request for more troops while the administration rethinks strategy in the wake of last month's Afghan elections, which have been racked by allegations of fraud.

It also comes as public support for the war is waning badly. In a NBC-Wall Street Journal poll conducted between last Thursday and Sunday, 59% of respondents said they were now "less confident" that the war would come to a successful conclusion. Just over half of those polled said they opposed adding more U.S. troops in the country, while more than a third favored an immediate withdrawal.

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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."

Defense Secretary Robert Gates has refused to make Gen. 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.

Sen. John Kerry of Massachusetts, chairman of the Senate Foreign Relations Committee, said he is braced for the Obama administration to table "a fairly significant reappraisal" of the U.S. strategy in Afghanistan. That reappraisal has been triggered, he said, by mounting concerns over the country's weak governance and the corruption shown in the recent election.

"The president is correct to step back and say, 'What are we going to do here?'" said Sen. Kerry. He said he has his own "serious questions" about whether more U.S. troops are really needed in Afghanistan and would like to hear directly from Gen. McChrystal.

Many of Mr. Obama's fellow Democrats are increasingly uneasy about his handling of the conflict. California's two senators, Dianne Feinstein and Barbara Boxer, have both expressed wariness over the current strategy and urged the administration to lay out a clear exit strategy. Sen. Russ Feingold of Wisconsin has argued that earlier troop build-ups in the country were counterproductive.

In the House, more than half of the Democratic caucus voted this summer in favor of an amendment, put forward by Massachusetts Rep. Jim McGovern, requiring the Pentagon to furnish an exit strategy for Afghanistan. The measure failed.

Democratic leaders have been trying to tamp down the signs of dissent within the party. Senate Majority Leader Harry Reid urged his caucus earlier this month to "just take it easy" and "wait until the president makes up his mind as to what he thinks should be done."

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Centrist Democrats like Rhode Island's Sen. Jack Reed want to replace the administration's strategy for Afghanistan with a hybrid Afghanistan policy designed to scale back American objectives in Afghanistan without letting the country fall apart.

These Democrats are leery of a troop increase, arguing that the main effort has to focus on building up the Afghan army while increasing the U.S. and NATO civilian presence in the country.

Sen. Reed has spoken in favor of a strategy that would relinquish the fight against the Taliban in many of the disputed areas of the country in order to focus on protecting key population centers.

Gen. McChrystal has advocated a similar strategy in his confidential assessment of the war. U.S. troops are already pulling out of some remote outposts in Afghanistan.

Republican lawmakers, who have been the most supportive of the Afghan war effort, are also beginning to push for testimony from the top commander on the ground.

Republican members of the Senate Armed Services Committee this week wrote a letter to the panel's chairman, Michigan Democrat Carl Levin, asking for a McChrystal hearing.

"The American people are due a full and public accounting of the challenges and commitments that lay before us," Arizona Sen. John McCain, the committee's senior Republican, wrote in the letter. In a written statement, Sen. Levin dismissed the request as premature.

In the House, Mr. Skelton is one of the most influential voices calling for hearings with Gen. McChrystal.

The lawmaker sent a formal request for such a hearing to Mr. Gates last month, writing that he believed Gen. McChrystal should appear before his panel at the end of the 60-day assessment, which was completed Aug. 30.

"There is significant interest in Congress and among the public in the outcome of General McChrystal's assessment and any resulting changes in our strategy or operations," Mr. Skelton wrote in the Aug. 13 letter. "A good way to address this desire for information would be to have General McChrystal appear at a hearing."

In an interview, Mr. Skelton said that he hasn't heard back from the Pentagon about his request, and warned that he might take stronger steps if his request was denied.

"They don't get a penny without us, and we of course make policy along with paying the bills," Mr. Skelton said.

Write to Yochi J. Dreazen at yochi.dreazen@wsj.com, Neil King Jr. at neil.king@wsj.com and Peter Spiegel at peter.spiegel@wsj.com