The Afghan government has agreed to waive customs fines for outbound U.S. military cargo, resolving, at least temporarily, a dispute that had threatened to delay and drive up the cost of the military drawdown.

The U.S.-led military coalition in Kabul issued a statement Thursday that Afghanistan’s Finance Ministry was relenting on an effort to collect $70 million in fines it says the United States owes for failing to properly fill out customs forms.

The dispute prompted the Afghan government to shut down the border last month for a few days, forcing U.S. commanders to rely more heavily on air transport, which is far more expensive than shipping equipment by land.

The demand, which some U.S. military officials saw as a shakedown, prompted influential U.S. lawmakers to threaten to withhold U.S. aid to Afghanistan.

Sen. Patrick J. Leahy (D-Vt.), the chairman of a subcommittee that has oversight of aid programs, proposed an amendment that would have deprived Afghanistan of $5 in future appropriations for every $1 it collected in customs fees. He called Kabul’s demand “beyond the pale.”

The International Security Assistance Force said in its statement that it was pleased that Kabul had decided to abide by a technical agreement signed during the early years of the Afghan war, which gave the United States great leeway in legal and bureaucratic matters.

“This agreement provides our forces with the freedom of movement necessary to effectively support our Afghan counterparts as they secure the Afghan people,” the coalition said in its statement.

Afghan officials said they have sought for years, largely in vain, to charge the U.S. military routine customs charges. Washington and Kabul have wrangled over the issue several times over the years. But last month’s spat was the most serious because Afghanistan had never before shut down the border to U.S. cargo.