"I don't think the way forward is to get an arms race going in Syria. There's a risk that that would undermine the conditions for a political process," Bildt told Swedish news agency TT.
Bildt said he feared a scenario where the US provided the militant groups with weapons on one side, while Russia supported the government of Syria on the other.
"There's no doubt that that would be very serious and have even more serious humanitarian consequences," Bildt said.
Bildt would prefer to see an international weapons embargo on Syria, TT reported.
US officials did not specify what type of military support Washington was considering, but US media reports said they included a limited no-fly zone over terrorist groups training camps, as well as small arms, ammunition and anti-tank weapons.
Syria has meanwhile dismissed the US accusation of chemical weapons use as "a statement full of lies."