Correction: An earlier version of this article misstated the Obama administration’s budget request for military and economic aid to Pakistan in fiscal 2013. The proposed amount is $2.2 billion, not $3.5 billion. This version has been corrected.

Trucks journey along a roadway at the Torkham border on May 20, 2012. There are no signs of Pakistan opening its border crossing to NATO trucks carrying essential supplies to Afghanistan, costing the United States an additional $100 million a month to fund alternative routes. (A Majeed/AFP/Getty Images)

Pakistan’s seven-month-long refusal to allow U.S. and NATO supplies to cross its territory into Afghanistan is costing the United States an additional $100 million a month to fund alternative routes, Defense Secretary Leon E. Panetta said Wednesday.

Panetta’s testimony to a Senate appropriations panel was the first time the Obama administration has put a dollar figure on the extra amount. Pakistan closed its border to NATO transit in November, after a U.S. cross-border air assault inadvertently killed 24 Pakistani soldiers.

Defense Department and Pakistani negotiators have agreed on a new payment structure for the transit, but Pakistan has also demanded an apology for the troop deaths. The Obama administration has expressed “regret” and offered condolences, but it has said that an apology is unnecessary for an incident in which Pentagon investigators found fault on both sides.

The apology issue has become a political lightning rod in Pakistan, where anti-American sentiment runs high. In the United States, Congress and the administration have grown increasingly irate over what is seen as Pakistani intransigence. During a visit to the region last weekend, Panetta said the United States was “reaching the limits of . . . patience” with Pakistan.

Asked by lawmakers whether he would recommend stopping U.S. aid to Pakistan, Panetta said, “I’d be very careful about, you know, just shutting it down.” Instead, he said without elaboration that he would place conditions on aid based on “what we expect them to do.” The administration requested about $2.2 billion in military and economic assistance for Pakistan for fiscal 2013.

Until the border closure, Pakistan was the main transit route for the vast bulk of U.S. and NATO supplies for the Afghanistan war, with goods arriving by ship at the Karachi port and trucked in cargo containers across the border. Most of the goods now enter Afghanistan from the north, via Russia and Central Asia, at significantly higher expense. The costs are expected to mount when U.S. troop withdrawals are stepped up later this year.