NAIROBI, Kenya — A month after the Trump administration formally lifted decades-old sanctions against Sudan, a top official said on Thursday that the United States would consider removing Sudan from its list of state sponsors of terrorism, a designation that has been in place since 1993.

The step, which is contingent on further cooperation by Sudan with Washington, would further demonstrate the striking turnabout in relations between the countries, a thaw that began under the Obama administration and a rare area in which the Trump administration has continued the approach of its predecessor.

Deputy Secretary of State John J. Sullivan said the United States was willing to consider removing Sudan from the its list of state sponsors of terrorism if Sudan continued to make progress on counterterrorism cooperation, human rights and other key issues. Syria, since 1974, and Iran, since 1984, are the other countries on the list.

Mr. Sullivan said he raised those issues in a two-day visit to Khartoum, the Sudanese capital. He is one of the highest-level officials to visit Sudan in a decade.