Secretary of State Hillary Rodham Clinton appealed to skeptical lawmakers for patience and support Thursday as the administration tries to mend a deep rift with Pakistan, encourage negotiations with U.S. enemies and prepare for the promised withdrawal of all American combat forces from Afghanistan by 2014.

“I will be the first to admit that working with our Afghan and Pakistani partners is not always easy,” Clinton told the House Foreign Affairs Committee. “But these relationships are advancing America’s national security interests, and walking away from them would undermine those interests.”

Despite what it sees as significant recent successes against al-Qaeda and refinements in its strategy leading to an eventual end of the Afghanistan conflict, the administration faces growing doubts among the public and in Congress about whether the war is winnable and flagging interest in spending more money and lives on it.

Clinton spoke positively of what she called a “fight, talk and build” strategy, in which intensified military strikes will “squeeze” Pakistan-based militants toward the negotiating table. She said that during a visit last week to Pakistan, she had “detailed and frank conversations” and that a page had been turned after relations deteriorated in the wake of public U.S. accusations of Pakistani support for the militants.

She also described recent U.S. efforts to persuade Afghanistan’s neighbors to support reconciliation efforts and to participate in cooperative regional trade. Clinton will attend a conference of regional governments next week in Istanbul that the administration hopes will result in pledges to bolster Afghanistan’s economy and promises not to support warring proxy forces there.

“This strategy requires resources,” Clinton said in addressing a committee that has approved tight restrictions on the administration’s proposed budget for Pakistan. “I can’t sugarcoat that fact.”

But lawmakers on both sides of the aisle seemed unimpressed. “It is hard to be optimistic,” Chairman Ileana Ros-Lehtinen (R-Fla.) said. “All the options on the table appear deeply unappetizing. All run the risk of being ineffectual, counterproductive or both.”

Rep. Howard L. Berman (Calif.), the ranking Democrat on the committee, said the administration should “reevaluate” all military assistance to Pakistan — more than $2 billion last year. At the same time, he said, “I continue to have reservations about efforts to reconcile with the Taliban and al-Qaeda-affiliated groups such as the Haqqani network.”

Clinton said that a meeting held by administration officials in the summer with a representative from the Haqqani network “was not a negotiation.” She said that there was “no follow-up meeting” and that the response from the Pakistan-based Afghan group — which U.S. military commanders have said is the most “active” in attacking American forces — “was an attack on our embassy.”

But the administration has said repeatedly that the Afghanistan war will ultimately end with a political agreement among warring Afghan ethnic and political groups. In addition to the August meeting with Ibrahim Haqqani, the brother of the organization’s patriarch, officials have held at least two meetings this year with a representative of the Quetta Shura, the Taliban umbrella group led by Mohammad Omar that is also based in Pakistan. “Negotiations would have to include the Quetta Shura,” Clinton said.

“We want to fight, talk and build — all at the same time,” she said. “Part of the reason for that is to test whether these organizations have any willingness to negotiate in good faith. There’s evidence going both ways.”

Clinton was accompanied on her recent visit to Pakistan by CIA Director David H. Petraeus and Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff. They outlined a new arrangement in which the administration would cease calling for the Pakistanis to begin a military offensive against Haqqani sanctuaries in the tribal region near the Afghanistan border. Instead, they asked Pakistan to help launch targeted strikes against Haqqani leaders and simultaneously assist in bringing them to the negotiating table.

The U.S. outreach last week essentially gave Pakistan the seat at the table that it has long sought. Although the hope is that talks will ultimately be facilitated by an outside negotiator such as the United Nations, initial discussions should include only direct participants in the war — Afghanistan, the Taliban, the United States and Pakistan, said a senior administration official, who spoke on the condition of anonymity Thursday to avoid preempting Clinton’s testimony.

Clinton also asked the Pakistanis to issue a public statement calling for the Taliban to begin serious negotiations, the official said.

The Istanbul regional meeting next week will include Iran and other countries in Central and South Asia, with the United States and European nations attending as “supporters.” That meeting will be followed by a much larger gathering Dec. 5 in Bonn, Germany, marking the 10th anniversary of the international conference that began after the overthrow of the Taliban government.

At a summit in Chicago in May, NATO hopes to mark major progress in peace negotiations and transition to Afghan security forces, leading to the withdrawal of international combat troops by the end of 2014.