Of particular concern, officials said, has been a rise in attacks by Taliban and other militants from remote and largely ungoverned tribal areas in Pakistan in eastern Afghanistan, where most of the American combat forces in the country are based.

"The border area is a problem," Defense Secretary Robert M. Gates told reporters after meeting on Tuesday with President Hamid Karzai of Afghanistan. Mr. Gates said more attacks were coming from across the border and from "Al Qaeda networks operating across the border."

On his first visit to Afghanistan since taking office six weeks ago, Mr. Gates flew by helicopter to a small joint American-Afghan base in Khost Province, less than a mile from the border.

A senior American military intelligence officer, speaking on condition of anonymity, said cross-border attacks had tripled in that part of the border region.

Staff Sgt. Ronald Locklear, one of the 120 American soldiers at the base, said fighters based in Pakistan "cross the border on a regular basis." He said the base was being hit by rocket and mortar fire at least once a week. Officials said they had evidence that Pakistani border guards ignored infiltration of Taliban fighters.

The senior American commander in Afghanistan, Lt. Gen. Karl Eikenberry, told reporters after meeting with Mr. Gates that he was hopeful that the Bush administration would seek a much larger aid package from Congress for the training of Afghanistan security forces and for reconstruction projects.

Other officials said that the total budget request was likely to be at least twice last year’s level of nearly $3 billion, but that the exact number had not been determined.

The resurgence in attacks by Taliban fighters and other militants began last summer and has continued in eastern Afghanistan even this winter, when fighting would normally subside, officials said.

While praising Pakistan as a "strong ally," Mr. Gates said the border problem "clearly has to be pursued with the Pakistani government."

General Eikenberry said that the "enemy is using both sides of the border" and that even after five years of pressing the Pakistani government to shut down Taliban infiltration, "there is no easy solution to the problem."

American commanders say the surge in cross-border attacks has coincided with an agreement reached last September in which the Pakistani government pulled back its soldiers in the North Waziristan region in return for a pledge from tribal elders not to shelter militants or allow them to engage in illegal behavior.

In the two months before the agreement, the senior American intelligence official said, there were 40 cross-border attacks in Khost and Paktika Provinces. But in the two months after the agreement there were 140 attacks.

Pakistan’s president, Gen. Pervez Musharraf, has sent 80,000 troops into the Waziristan tribal areas. On Tuesday, shortly before Mr. Gates arrived on the Afghan side of the border, General Musharraf’s military announced that it had destroyed three compounds in South Waziristan used by militants as hide-outs.

In a strike shortly before 7 a.m., helicopters hovering above a complex of five compounds fired a volley of missiles, Pakistani officials said. Three compounds were destroyed, but officials gave different figures for the number of dead.

A security official in Peshawar said at least 20 militants had been killed. Maj. Gen. Shaukat Sultan, the chief military spokesman, said 25 to 30 had been killed. But later he told state-run television that the airstrike had killed "eight militants, along with their local supporters."

He said that no ground troops had been involved and that "no high-value targets were believed to be there," a reference to top Qaeda leaders like Osama bin Laden and Ayman al-Zawahri.

Eight bodies were retrieved from the rubble, five of them Afghans and three from the local Kikari Mehsud tribe. Ten wounded people were taken to private hospitals in North Waziristan, officials said.

Addressing a military conference in Rawalpindi, General Musharraf reiterated his resolve to fight terrorism and militancy in his country. "Any hide-out or sanctuary being used by terrorists or miscreants shall be knocked out, wherever it is found," the state-run news agency quoted him as saying.

In Afghanistan, General Eikenberry, who is leaving his post this month as the senior American commander in the country, said American and NATO troops as well as Afghan Army units had inflicted heavy casualties on the Taliban, which he said remained too weak to undertake anything other than hit-and-run attacks or suicide bombings.

The American military intelligence officer disclosed for the first time statistics on the rise in insurgent attacks last year. There were 139 suicide attacks, up from 27 in 2005, and use of roadside bombs more than doubled, to 1,677 last year from from 783 in 2005. The number of what the military calls "direct attacks," meaning attacks by insurgents using small arms, grenades and other weapons, increased to 4,542 last year from 1,558 in 2005.

But even with 21,000 American troops and an additional 20,000 soldiers from other NATO countries, military officials are pushing for more forces before spring, when the Taliban is widely expected to intensify its attacks.

General Eikenberry is seeking to extend the deployment of a 1,200-soldier American battalion, which is halfway through a four-month deployment. The unit, part of the 10th Mountain Division, based in Fort Drum, N.Y., is scheduled to go to Iraq in eight months, but General Eikenberry has argued that he needs the unit to remain in Afghanistan.

Asked about increasing American troop levels in Afghanistan, Mr. Gates said that if military commanders sought more, "I would be strongly inclined to recommend that to the president."

He also urged other NATO counties to fulfill their pledges to send more troops and equipment to Afghanistan. NATO governments still have not sent the additional 1,200 troops that Gen. David Richards, the British commander of NATO forces here, has requested to serve as a reserve force he can send wherever violence flares around Afghanistan, according Mark Laity, a NATO spokesman.

Salman Masood contributed reporting from Islamabad, Pakistan, and Ismail Khan from Peshawar.