The precise reasons for the increase in rocket fire are unclear. Whether the surge in attacks indicates Pakistani military retaliation, an emboldened insurgency, some degree of both or some other factors cannot be determined from the data alone.

The attacks covered by the military’s data included those on three American-Afghan outposts — Forward Operating Base Tillman, Combat Outpost Boris and Combat Outpost Margah — and usually involved two to four rockets each, officers said. The incoming fire has continued through recent days, including an attack last Friday that set buildings ablaze at Forward Operating Base Tillman.

The data release does not include attacks against American military positions in provinces other than Paktika or against Forward Operating Base Lilley, in the same province, which is used by the C.I.A.

But it does include attacks from several insurgent positions just inside Afghanistan, some within 200 yards of the border, from where rocket crews fire and then rush to Pakistan.

There were at least 102 of these so-called close-border attacks against the same outposts since May, including one on Oct. 7 that the American military called the largest and most coordinated insurgent operation in the province since 2009. Last year, during the same period in the same places, there were 13 close-border attacks. Most of the indirect-fire attacks, officers said, have been with 107-millimeter rockets, which have a range of about five miles. They were designed in China in the 1960s but have been reproduced by several nations. The exact source of the rockets was not immediately clear. Chunks of expended munitions examined by The New York Times had minimal markings, preventing a ready identification.

The perils and sensitivities surrounding the rocket fire starkly underscored the longstanding difficulties faced by the latest rotation of soldiers in the Afghan war, who are in front-line positions built by previous units, under fire, but with restrictions on firing back or when planning operations to deter more attacks.

Another officer, who analyzed each incident, said attacks often come from positions next to Pakistani military or Frontier Corps border posts. He said there has been no sign of Pakistani units trying to stop the firing, or of willingness to help American units identify who is shooting at them.