Syria said the strikes were a "blatant attack on forces fighting terrorism", while Russia said it was "unacceptable" and a violation of Syrian sovereignty.
The convoy was hit on Thursday, May 18 as it neared a group of U.S.-backed rebels and a Western special forces unit in Tanf.
The U.S. said Russia was told in advance and that warning shots were ignored.
The U.S.-backed Maghaweer al-Thawra rebel faction said that the convoy had been about 27km (17 miles) away and contained four tanks.
A U.S. defence official said the convoy had not responded to numerous warnings that it was "getting too close to coalition forces".
The U.S.-led coalition said the convoy that was attacked consisted of Syrian and Iranian-backed militias.
But a statement on Syrian state news agency Sana said that the air strikes at 16:30 (13:30 GMT) on Thursday had targeted one of the "military points" of its army.
It said there had been "a number" of deaths and "some material losses" and that the army would not be intimidated by attempts to stop it performing its counter-terrorism duties.
Russian Deputy Foreign Minister Gennady Gatilov also said the strikes had targeted "the Syrian armed forces".
He said: "This is completely unacceptable, this is a breach of Syrian sovereignty." Mr Gatilov added: "Any military action that leads to escalation of the situation in Syria undoubtedly affects the course of the political process."
Rebel officials said earlier this week that hundreds of troops and militiamen were advancing into the sparsely-populated desert region near the Jordan border, in an apparent attempt to halt recent rebel gains against so-called Islamic State (IS).
The U.S.-led coalition said that, ahead of the air strikes, a telephone call had been put into the Russian military, which backs President Bashar al-Assad. That was followed by a "show of force" by aircraft overhead and warning shots, the officials said.
"Then there was finally a strike against the lead portion of that movement."
A U.S. defence official told the AFP news agency that the strike did not signal a strategic shift for the coalition, which has focused on battling IS and has tried to avoid intervening in Syria's civil war.
U.S.-led troops helped repel a major IS attack on Tanf last month, while Russian warplanes bombed the base in June 2016.