WASHINGTON — Gen. David Petraeus, in his first appearance in Washington since taking over as the top war commander in Afghanistan, is laying out a mostly upbeat assessment of military progress that should allow the United States to begin withdrawing forces this summer, despite predictions that the wounded Taliban insurgency will mount an especially bloody fight this spring.

No one is calling it the Taliban’s last stand, but U.S. officials say this is the year that the insurgency will be tamed on the battlefield and at the bargaining table.

Petraeus met privately with President Obama and Defense Secretary Robert Gates on Monday, the start of a full week of testimony and other events.

In a statement describing the meeting, the White House said the three discussed “the effectiveness of the military surge, the growth of the Afghan National Security Forces and President (Hamid) Karzai’s expected March 21 announcement on beginning transition to Afghan security lead.”

The optimism comes with some significant caveats, but it still marks a significant turn from worries a year ago about the strength and durability of the Taliban-led insurgency as the first of Obama’s 30,000 additional troops worked to take and hold Taliban strongholds in southern Afghanistan.

Sen. John McCain of Arizona, the top Republican on the Armed Services Committee, said he expects Petraeus to “talk about the success they have had on the ground. Every observer who has gone over there has been impressed with that success.” On the other hand, Petraeus will face tough questions from the committee about corruption in Karzai’s government and the situation in Pakistan.

“I expect certainly some skepticism on both sides of the aisle,” McCain said in an interview. “I don’t see any kind of pressure to withdraw immediately.”

Obama wants to begin reducing U.S. forces in Afghanistan in July with the aim of a full security transfer to the Afghans by the end of 2014 — a goal that Obama, Petraeus and Gates discussed on Monday.

Petraeus was expected to caution that the transition of control to Afghan security forces will be slow and difficult as the Kabul government struggles to find its footing. And commanders are planning for a brutal spring fighting season as insurgents try to regain their place and test the fledgling Afghan troops.

“There is no question that the injection of 30,000 additional American troops has had an impact on the Taliban’s ability to operate,” said Karl F. Inderfurth, a former senior State Department diplomat for South Asia. “The situation on the ground will almost certainly be the most promising part of the story that General Petraeus can tell.”

Other difficult struggles will determine success, including the insurgents’ safe havens in Pakistan, the reconciliation process with more moderate Taliban, and establishment of a more capable government, said Inderfurth, who is now with the Center for Strategic and International Studies.