KABUL — President Obama and the Afghan leader, Hamid Karzai, had what a US official called a ‘‘serious and positive’’ discussion on Wednesday night that the Afghans confirmed had made progress toward resolving an increasingly acrimonious dispute that had their two governments and their militaries at loggerheads for weeks over rules for detaining terrorism suspects in the field.

In a video teleconference, the two had a wide-ranging conversation touching almost every hot-button issue that has complicated the US plans to draw down its forces here, US and Afghan officials said.

Most important, they began to resolve the two countries’ differences on rules for indefinitely detaining terrorism suspects without trial, known as administrative detention, officials from the two countries said. US military commanders insist on assurances that terrorism suspects they detain in the field will not be summarily released.

The Afghan Constitution and laws do not provide explicitly for indefinite detention, but Karzai has now ordered his judiciary ‘‘to come up with a legal framework that allows us to keep those people who pose a serious security threat,’’ Aimal Faizi, the president’s spokesman, said.

The Americans have refused to turn over the last 600-plus prisoners they are holding at Parwan, the US-built detention center, until the issue is resolved.

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