The number three official at the State Department, David Hale, met in Washington with Sudanese Foreign Minister Asma Mohamed Abdalla.
They discussed "relevant policy and statutory criteria for rescission of Sudan's State Sponsor of Terrorism designation," department spokeswoman Morgan Ortagus said in a statement.
Since 1993 Sudan has been on the list of countries the United States deems backers of terrorism for having granted safe haven to Osama bin Laden.
But in recent years Washington has allowed progressively warmer relations with Sudan, citing what it called progress in the fight against terrorism, until in 2017 it lifted a 20-year-old economic embargo.
Since the overthrow last April of longtime dictator Omar al-Bashir and the emergence of a transitional government strongly backed by Washington, the process of removing Sudan from the blacklist could go even faster.
For Sudan officials, who see winning Washington's blessing as important for economic growth, removal from the list is key.
Hale, whose title is under secretary for political affairs, believes that "compensation for the victims of terrorism remains a priority for the US government," Ortagus said.
Compensation would essentially consist of financial reparations to families of people killed or injured in attacks against the US embassies in Tanzania and Kenya that were carried out by al-Qaeda in 1998. US judges have said Sudan is effectively to blame for the blasts.
During a historic visit to Washington in December, Sudanese Prime Minister Abdalla Hamdok said progress was being made on this sensitive issue.
Court battles and negotiations are underway on damages, which have been set by US courts in the billions of dollars. An appeal by Sudan is to go before the Supreme Court in February.