Tensions have been rising in northeastern Syria in recent months as the Syrian military has cut off American access to several areas.
State news agency SANA quoted an unnamed Syrian military official as saying a U.S. helicopter gunship attacked an army checkpoint in the village of Tal Dahab, near the town of Qamishli, at around 9:45 a.m. (0645 GMT). The official said a Syrian soldier was killed and two others were wounded.
SANA said the Syrian army prevented an American convoy from passing through.
The U.S. military said a joint force made up of U.S.-led coalition forces and allied Syrian Kurdish-led fighters encountered a Syrian army checkpoint after carrying out a patrol against the Islamic State group. It said they were granted safe passage.
It said the patrol then came under small arms fire from the vicinity of the checkpoint and returned fire. There were no casualties among U.S.-led coalition forces or the Kurdish-led fighters, the statement said.
It denied a helicopter gunship attacked the Syrian army checkpoint.
Hundreds of U.S. troops are stationed in northeastern Syria, working with their local partners from the Kurdish-led Syrian Democratic Forces to combat the Islamic State group.
The attack occurred during the 25th such patrol, the military reported in a statement posted on Twitter.
The statement said Turkish troops had responded to the attack and that an operation was continuing.
Associated Press write Suzan Fraser contributed to this report from Ankara, Turkey.