A senior American military commander is expected to travel to Pakistan this month in what Obama administration officials say is the first step toward thawing a strategic relationship that has been in effect frozen for more than two months.

Gen. James N. Mattis, the head of the military’s Central Command, will meet Gen. Ashfaq Parvez Kayani, the Pakistani Army chief of staff, to discuss the investigations of an exchange of fire at the Afghan border that killed 24 Pakistani soldiers, as well as new border coordination procedures to prevent a recurrence of the episode.

General Mattis’s visit, the first by a high-ranking American official since the cross-border confrontation in November, was to have begun Thursday, but has been postponed by at least a week pending what is expected to be a spirited debate in the Pakistani Parliament over a new security policy toward the United States.

Pakistani and American officials are quietly optimistic that both events will trigger a chain of public engagement and private negotiations that will reboot the two nations’ frayed strategic relationship, although along more narrowly defined lines than before.

Pakistani officials say they will probably reopen NATO supply lines running through their territory, which have been closed for more than two months. The State Department is supporting a proposal circulating in the administration for the United States to issue a formal apology for the deaths of the Pakistani soldiers in the Nov. 26 airstrike by American gunships.

“We’ve felt an apology would be helpful in creating some space,” said an American official who has been briefed on the State Department’s view and who spoke on the condition of anonymity as internal discussions continued.

Soon after the lethal airstrike, the White House decided that President Obama would not offer formal condolences to Pakistan, overruling State Department officials who argued for such a show of remorse to help salvage relations. Pentagon officials had balked, saying the statements from other American officials had been sufficient. Some administration aides said at the time that they worried that if Mr. Obama decided to overrule the military and apologize to Pakistan, it could become ammunition for his Republican opponents in the presidential campaign.

A State Department spokeswoman, Victoria Nuland, would not comment on the proposal on Monday.

American election politics are also on the mind of Pakistani strategists. A senior security official in Islamabad, speaking on the condition of anonymity because he is not authorized to speak publicly on the issue, said the military was cognizant of Mr. Obama’s domestic political constraints, and noted that Pakistan may also have elections this year, probably in the fall.

“Unfortunately there is election fever on both sides of the divide this year,” the official said. “That limits the room for maneuver.”

The director of the State Department’s policy planning office, Jake Sullivan, signaled last month that relations could improve soon.

Speaking to foreign journalists in Washington on Jan. 25, Mr. Sullivan said, “We will see over the course of the next several weeks an intensive period of work to deal with the very real issues that continue to exist between the United States and Pakistan in our relationship.”

American officials in Washington said the thaw had already started, unofficially. Relations between the C.I.A. and Pakistan’s Inter-Services Intelligence Directorate, or ISI, had slowly improved since the nadir after the raid that killed Osama bin Laden last May, they said.

Intelligence officials from the two countries have resumed discussions about “joint targeting,” officials here added — probably a reference to C.I.A.-directed drone strikes in Pakistan’s tribal belt. On the military side, Pakistan’s generals had started discussions over border coordination and the resumption of Coalition Support Funds, the main United States subsidy to Pakistani military operations.

A senior Pakistani security official also struck a cautiously positive note. “We have to meet, we have to talk, we have to bring this relationship back on track,” he said. “Both of us need each other. But from now on there will be no free rides, no carte blanche — things need to be institutionalized.”