Gen. David H. Petraeus told lawmakers Tuesday that the U.S. and NATO forces he commands in Afghanistan have halted the Taliban’s momentum in much of the country, but he predicted difficult fighting ahead as the radical Islamist insurgents try to regain lost territory in a spring offensive.

Testifying before the Senate Armed Services Committee, Petraeus said that the “hard-fought achievements in 2010 and early 2011” by U.S. and NATO forces have permitted a recommendation to shift lead security responsibility to Afghan forces in several provinces this spring.

He said these achievements also are important as he prepares to “provide options and a recommendation to President Obama for commencement of the drawdown of the U.S. surge forces in July.” He referred to Obama’s Dec. 1, 2009, speech at the U.S. Military Academy in which he pledged to start withdrawing U.S. troops from Afghanistan in July 2011 at a pace to be determined by conditions on the ground.

In addition, Petraeus said, “the progress achieved has put us on the right azimuth to accomplish the objective agreed upon at last November’s Lisbon Summit, that of Afghan forces in the lead throughout the country by the end of 2014.”

The general’s comments come amid declining U.S. support for the Afghanistan war effort, which began in the fall of 2001 following al-Qaeda’s Sept. 11 terrorist attacks. According to a new Washington Post-ABC News poll, nearly two-thirds of Americans now say the war in Afghanistan is no longer worth fighting.

In an opening statement at Tuesday’s hearing, Sen. John McCain (R-Ariz.) said that in view of the poll, the next few months could be “decisive” as winter turns to spring and NATO forces “face a renewed Taliban offensive to retake territory lost on the battlefield.”

McCain, the top Republican on the committee, said the United States “needs to be exceedingly cautious about the withdrawal of U.S. forces” starting in July. “We should not rush to failure, and we should cultivate strategic patience,” he said.

Sen. Carl M. Levin (D-Mich.), the committee chairman, said the success of the U.S. mission in Afghanistan depends on the growth and capability of the Afghan security forces. He pointed to what he called a hopeful sign in “the increasing support of the Afghan people” for their security forces. He agreed that this spring’s fighting season could be an “acid test” as the Taliban tries to reverse recent losses.

Sen. Joseph I. Lieberman (I-Conn.) lamented the decline in U.S. popular support even though “we are succeeding in the Afghan war.” He attributed such sentiments more to continuing frustration over the domestic economy than to the actual situation in Afghanistan, and he said that “we have to remind the American people why we are in Afghanistan, why it’s worth it, and we are succeeding.”

In response to questions, Petraeus said he has not yet decided on the scope of the withdrawals that are to begin in July. But he expressed support for the concept of starting the drawdown then because “it undercuts the narrative of the Taliban that we will be there forever” and sends a message of urgency to the Afghan government.

He said he has requested resources to increase the Afghan security forces by 70,000, building on the growth “in number and capability” of those forces in the last couple of years. He said the growth is projected to bring the size of the Afghan forces to as many as 378,000, with a floor of at least 352,000.

Petraeus said the assessment by the NATO command in Afghanistan is that “the momentum achieved by the Taliban in Afghanistan since 2005 has been arrested in much of the country and reversed in a number of important areas.” He added: “However, while the security progress achieved over the past year is significant, it is also fragile and reversible. Moreover, it is clear that much difficult work lies ahead with our Afghan partners to solidify and expand our gains in the face of the expected Taliban spring offensive.”

Petraeus said U.S. and NATO forces, working with Afghan partners, have “stepped up the tempo of precise, intelligence-driven operations to capture or kill insurgent leaders.” He said about 360 “targeted insurgent leaders” are killed or captured in a typical three-month period. He also cited successes in clearing the Taliban from long-held safe havens, including “such critical areas as the districts west of Kandahar city that were the birthplace of the Taliban movement, as well as important districts of Helmand Province.”

A program to reintegrate “reconcilable” insurgents has also shown promise, Petraeus said, noting that “we and our Afghan partners cannot just kill or capture our way out of the insurgency in Afghanistan.” He said that “some 700 former Taliban have now officially reintegrated with Afghan authorities, and some 2,000 more are in various stages of the reintegration process.”

The general expressed concern, however, that “levels of funding for our State Department and [U.S. Agency for International Development] partners will not sufficiently enable them to build on the hard-fought security achievements of our men and women in uniform.” He warned the committee, “Inadequate resourcing of our civilian partners could, in fact, jeopardize accomplishment of the overall mission.”