Blinken is the first US official to publicly confirm contacts between the Biden administration and Hayat Tahrir al-Sham, or HTS, which led a coalition of armed opposition groups that ousted Assad from power last Sunday.
The US has long designated the group as a foreign terrorist organisation.
Speaking at a news conference in Aqaba, Jordan, Blinken would not discuss details of the contacts but said it was important for the US to convey messages to the group about its conduct and how it intends to govern in a transition period.
"Yes, we have been in contact with HTS and with other parties," Blinken said.
He added that "our message to the Syrian people is this: We want them to succeed and we're prepared to help them do so".
Turkish Foreign Minister — Secretary Antony Blinken (@SecBlinken) @HakanFidan and I met to discuss the situation in Syria and the importance of a Syria-led and Syrian-owned transition. We also spoke about the need to protect the rights and freedoms of Syrians, including members of minorities, during this pivotal time. pic.twitter.com/rSjmn4gk3iDecember 13, 2024
HTS, which was once an affiliate of al-Qaida, has been designed as a foreign terrorist organisation by the State Department since 2018.
That designation carries with it severe sanctions, including a ban on the provision of any "material support" to the group or its members.
The sanctions do not, however, legally bar US officials from communicating with designated groups.
In an interview Saturday on Syrian television, the group's leader, Ahmad al-Sharaa, formerly known as Abu Mohammed al-Golani, did not address any direct contact with the United States, but said the new authorities in Damascus, the capital, are in touch with Western embassies.
HTS has worked to establish security and start a political transition after seizing Damascus and has tried to reassure a public both stunned by Assad's fall and concerned about extremist jihadis among the rebels. Insurgent leaders say the group has broken with its extremist past.
Al-Sharaa appeared in a video message Friday congratulating "the great Syrian people for the victory of the blessed revolution".
US officials say al-Sharaa has been making welcome comments about protecting minority and women's rights but remain sceptical that he will follow through on them in the long run.
On Friday, the rebels and Syria's unarmed opposition worked to safely turn over to US officials an American man who had been imprisoned by Assad.
US officials are continuing their search for Austin Tice, an American journalist who disappeared 12 years ago near Damascus.
"We have impressed upon everyone we've been in contact with the importance of helping find Austin Tice and bringing him home," Blinken said.