Washington is scrapping a long-standing reward for the arrest of Syria's new leader, a senior US diplomat said Friday, following "positive messages" from a first meeting that included a promise to fight terrorism.

Barbara Leaf, Washington's top diplomat for the Middle East, made the comments after her meeting with Ahmed al-Sharaa in Damascus -- the first formal mission to Syria's capital by United States diplomats since the early days of Syria's civil war.

The lightning offensive that toppled president Bashar al-Assad on 8 December was led by the Islamist Hayat Tahrir al-Sham (HTS), which is rooted in Al-Qaeda's Syria branch but has sought to moderate its image in recent years.

Leaf's meeting with HTS chief Sharaa came despite Washington's six-year-old designation of his group as a terrorist organisation.

"Based on our discussion, I told him we would not be pursuing the Rewards for Justice reward offer," Leaf told reporters.

After their talks, "it's a little incoherent, then, to have a bounty on the guy's head," she said, welcoming the messages from him.