Syria said the strikes were a "blatant attack on forces fighting terrorism", while Russia said they breached the country's sovereignty.
The convoy was hit on Thursday as it neared a group of US-backed rebels and a Western special forces unit in Tanf.
The US said Russia was told in advance and that warning shots were ignored.
Russia's Deputy Foreign Minister Gennady Gatilov said the strikes were "completely unacceptable", according to state-run news agency Ria Novosti.
He was quoted as saying in Geneva that any military action leading to an escalation of the conflict would have an impact on the political process.
The US-backed Maghaweer al-Thawra rebel faction said that the convoy had been about 27km (17 miles) away and contained four tanks.
A US defence official said the convoy had not responded to numerous warnings that it was "getting too close to coalition forces".
The US-led coalition said the pro-regime forces consisted of Syrian and Iranian-backed militias and "posed a threat to US and partner forces".
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.
The Syrian Observatory for Human Rights, a UK-based monitoring group, reported that eight people were killed. It said most of them were not Syrian.
Mr Gatilov also condemned a US-led coalition strike on Wednesday that reportedly killed dozens of civilians. The coalition has denied the attack occurred.
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 US-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 US 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.
US-led troops helped repel a major IS attack on Tanf last month, while Russian warplanes bombed the base in June 2016.