A US-led coalition has provided air support for Kurdish and rebel militia fighting IS since September 2014, but has not struck regime positions.
White House spokesman Josh Earnest said Assad's regime could be targeted if it attacked the new US-backed forces.
The United States, Earnest said, was "committed to using military force where necessary to protect the coalition-trained and equipped Syrian opposition fighters."
There was no official reaction from the Syrian government on Tuesday, but a political figure close to the regime told AFP that the US had "relayed a message to Damascus not to worry about these statements".
"It's about hitting Al-Nusra hard, not the Syrian army," he said.
Dubbed the "New Syrian Force" by Washington, the 54-strong rebel unit entered northern Syria in mid-July as part of US efforts to counter the powerful Islamic State jihadist group.
The force includes fighters from Division 30, based in Syria's northern province of Aleppo.
Despite Al-Nusra's fierce hostility to the rival jihadists of IS, the unit soon came under attack from the Al-Qaeda loyalists.
- Al-Nusra 'hunting down' rebels -
On Tuesday, the jihadists raided a camp for internally displaced people in Qah, capturing another five Division 30 men.
The Observatory chief said Al-Nusra was "hunting down" US-backed rebels in both Idlib province, where Qah is located, and in neighbouring Aleppo province.
The raids came less than a week after Al-Nusra seized eight Division 30 rebels in Aleppo province, the Observatory said, in a report that drew a denial from the Pentagon.
Two days later, Al-Nusra launched an assault on Division 30's Aleppo headquarters and were only repulsed with the help of US air strikes.
On Monday, Washington said it was prepared to expand those strikes to the Syrian regime, should it attack any of the US-trained units.
Charles Lister, an analyst at the Doha Brookings Centre, said the US statement was a "big shift in US policy" but that it would not translate into a significant change on the ground.
With the US-trained force deployed in border areas where there is limited regime activity, Lister said there was a slim chance of confrontation with government forces.
"It is extremely unlikely, at least for the next six months, that any situation will arise where the US will have to fight against the regime or strike it," Lister told AFP.
- 'Not a turning point' -
A Syrian military source, speaking on condition of anonymity, also played down the US warning.
"The American threats are nothing more than media statements," the source, speaking from Damascus, told AFP.
Although he would not explicitly rule out the possibility of strikes -- saying "everything is possible in war" -- he said other statements about US military action in Syria were not carried out.
"Three years ago, there were statements about a buffer zone, but hopes are one thing and reality is another," he said.
Bassam Abu Abdullah, director of the Damascus Centre for Strategic Studies, also brushed off the US statement and said it was "not a turning point".
"We don't expect anything else from the Americans," Abu Abdullah said.
He said such a small group of rebel fighters inserted into northern Syria "would not change the calculations there" and demonstrated that "the Americans are not serious about fighting IS".
State-run newspaper Al-Thawra published a scathing editorial on Tuesday saying the "terrorists that Washington wants to defend are simply another face of the extremism that Syria has been suffering from".
"America's insistence at defending those it has trained confirms the lie that it is fighting Daesh," it wrote, using an Arabic acronym for IS.
Syria's conflict began with anti-government protest in March 2011, but a brutal regime crackdown saw it spiral into a multi-front war that has killed more than 230,000 people.