The proposal, described by American officials in Washington and Afghanistan, would escalate military activities inside Pakistan, where the movement of American forces has been largely prohibited because of fears of provoking a backlash.

The plan has not yet been approved, but military and political leaders say a renewed sense of urgency has taken hold, as the deadline approaches for the Obama administration to begin withdrawing its forces from Afghanistan. Even with the risks, military commanders say that using American Special Operations troops could bring an intelligence windfall, if militants were captured, brought back across the border into Afghanistan and interrogated.

The Americans are known to have made no more than a handful of forays across the border into Pakistan, in operations that have infuriated Pakistani officials. Now, American military officers appear confident that a shift in policy could allow for more routine incursions.

America’s clandestine war in Pakistan has for the most part been carried out by armed drones operated by the C.I.A.

Additionally, in recent years, Afghan militias backed by the C.I.A. have carried out a number of secret missions into Pakistan’s tribal areas. These operations in Pakistan by Afghan operatives, known as Counterterrorism Pursuit Teams, have been previously reported as solely intelligence-gathering operations. But interviews in recent weeks revealed that on at least one occasion, the Afghans went on the offensive and destroyed a militant weapons cache.

The decision to expand American military activity in Pakistan, which would almost certainly have to be approved by President Obama himself, would amount to the opening of a new front in the nine-year-old war, which has grown increasingly unpopular among Americans. It would run the risk of angering a Pakistani government that has been an uneasy ally in the war in Afghanistan, particularly if it leads to civilian casualties or highly public confrontations.

Still, one senior American officer said, “We’ve never been as close as we are now to getting the go-ahead to go across.”

The officials who described the proposal and the intelligence operations declined to be identified by name discussing classified information.

Ground operations in Pakistan remain controversial in Washington, and there may be a debate over the proposal. One senior administration official said he was not in favor of cross-border operations — which he said have been generally “counterproductive” — unless they were directed against top leaders of Al Qaeda. He expressed concern that political fallout in Pakistan could negate any tactical gains.

Still, as evidence mounts that Pakistani troops are unlikely to stage a major offensive into the militant stronghold of North Waziristan, where Al Qaeda’s top leaders are thought to be taking shelter, United States commanders have renewed their push for approval to send American commando teams into Pakistan.

In announcing the results of a review of the strategy in Afghanistan, Obama administration officials said they were considering expanded American operations to deal with threats inside Pakistan. They offered no specifics.

In interviews in Washington and Kabul, American officials said that officers were drawing up plans to begin ground operations to capture or kill leaders from the Taliban and the Haqqani network. American officers say they are particularly eager to capture, as opposed to kill, militant leaders, who they say can offer intelligence to guide future operations.

Even before finalizing any plans to increase raids across the border, the Obama administration has already stepped up its air assaults in the tribal areas with an unprecedented number of C.I.A. drone strikes this year. Since September, the spy agency has carried out more than 50 drone attacks in North Waziristan and elsewhere — compared with 60 strikes in the preceding eight months.

In interviews, the officials offered a more detailed description of two operations since 2008 in which Afghans working under the direction of the C.I.A. — a militia called the Paktika Defense Force — crossed the border into Pakistan. They also offered a richer account of the activities of these militia groups throughout the country.

According to an Afghan political leader, one of the raids was initiated to capture a Taliban commander working inside Pakistan. When the Afghan troops reached the compound, they did not find the Taliban commander, but the Pakistani militants opened fire on them, the Afghan said.

An American official disputed this account, saying that the C.I.A. militias are not sent over the border to capture militant leaders, but merely to gather intelligence.

In a second raid, the Paktika militia attacked and destroyed a Taliban ammunition depot and returned to base, officials said. Both of the C.I.A.-backed raids were aimed at compounds only a few miles inside Pakistani territory.

The Paktika Defense Force is one of six C.I.A.-trained Afghan militias that serve as a special operations force against insurgents throughout Afghanistan. The other militias operate around the cities of Kandahar, Kabul and Jalalabad as well as in the rural provinces of Khost and Kunar.

One American service member, speaking on the condition of anonymity, said the C.I.A.-backed militia near Khost had recently deployed in the mountains along the Pakistan border, where it would spend the winter trying to intercept Taliban fighters. So far, the C.I.A.-backed force has proven effective, he said.

“The rockets we endured for the past seven months suddenly dried up,” the service member said.

In the past, the American military has had only limited success in its few cross-border operations. In October, an American military helicopter accidently killed a group of Pakistani soldiers during a flight over the border in pursuit of militants. The episode infuriated Pakistan’s government, which temporarily shut down American military supply routes into Pakistan. Several fuel trucks sitting at the border were destroyed by insurgents, and American officials publicly apologized.

Two years earlier, in September 2008, American commandos carried out a raid in Pakistan’s tribal areas and killed several people suspected of being insurgents. The episode led to outrage among Pakistan’s leaders — and warnings not to try again.

Mark Mazzetti reported from Washington, and Dexter Filkins from Kabul, Afghanistan. Eric Schmitt contributed reporting from Washington.