Barbara Leaf, the top US diplomat for the Middle East, said she told Sharaa of the "critical need to ensure terrorist groups cannot pose a threat inside of Syria or externally, including to the US and our partners in the region."
"Ahmed al-Sharaa committed to this," Leaf told reporters after the meeting in Damascus.
"Based on our discussion, I told him we would not be pursuing the Rewards for Justice reward offer," she said.
The FBI in 2017 put up a $10 million reward for information leading to the arrest of Sharaa, earlier known by his war name Abu Mohammed al-Jolani, pointing to his swearing of allegiance to Al-Qaeda.
Leaf, part of the first formal visit by US diplomats to Damascus since the early days of the brutal civil war, said that Sharaa "came across as pragmatic" and that their talks were "quite good, very productive, detailed."
"We welcomed positive messages" from Sharaa since his Islamist-rooted HTS rebels toppled strongman Bashar al-Assad, Leaf said.
"We will be looking for progress on these principles and actions, not just words," she said.
Sharaa and his rebels, Hayat Tahrir al-Sham, remain on Washington's terror blacklist. Leaf did not comment on the designation but said that after her discussions with Sharaa, "it's a little incoherent, then, to have a bounty on the guy's head."
Sharaa has spoken of inclusion and disbanding rebel factions. Leaf said she reinforced "the importance of inclusion and broad consultation during this time of transition."
"We fully support a Syrian-led and Syrian-owned political process that results in an inclusive and representative government which respects the rights of all Syrians, including women, and Syria's diverse ethnic and religious communities."
On Friday, thousands of Syrians held a celebration at Ummayad Square in central Damascus, in an event called for by Hayat Tahrir al-Sham (HTS) which toppled Bashar al-Assad regime on Dec 8. Speakers blared revolutionary songs, while people waved the newly adopted Syrian flag and chanted slogans in support of the government and against Assad.
The crowd was a mix of people from different walks of life and backgrounds: armed men in military fatigues, women - both with and without headscarves - and children.
Maram, 62, said that her four children had fled Syria 11 years ago and settled in Germany and Hungary after two of her sons were detained and tortured. She has not seen them since, but they plan to return to their country to help rebuild it, she said.
"The country has been completely destroyed in every aspect," she said, adding she hoped HTS could improve things, but was watchful. "We were not accustomed to freedom or governing our own country, so we will continue to monitor until we reach our goal."
There is widespread apprehension among Syrians that the new administration will gravitate towards hardline religious rule, marginalising minority communities and excluding women from public life.
Obaida Arnout, a spokesperson for the Syrian transitional government, said this week that women's "biological and physiological nature" rendered them unfit for certain governmental jobs. (AFP)
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