The two "discussed the need to urgently end the conflict in Sudan and enable unhindered humanitarian access, including cross border and cross line, to alleviate the suffering of the Sudanese people," spokesman Matthew Miller said in a statement.
In a roughly 30-minute phone call, Blinken "also discussed the resumption of negotiations in the Jeddah platform and the need to protect civilians and deescalate hostilities in El-Fasher, North Darfur," Miller said.
In mid-April, the United States said that peace talks on Sudan's war would be hosted by Saudi Arabia in its city of Jeddah within the coming three weeks, though a date for discussion has yet to be announced.
At least 134 people have died in two weeks in fighting that has raged in the city of El-Fasher, according to a toll published on Sunday by Doctors Without Borders (MSF).
Since April 2023, Sudan has been riven by war between the army, led by Burhan, and his former deputy, Mohamed Hamdan Daglo, who commands the paramilitary Rapid Support Forces (RSF).
El-Fasher in North Darfur is the only state capital in the vast western region not under RSF control, and is a key humanitarian hub for a region on the brink of famine.
It has seen sporadic clashes since the war broke out, but fierce fighting reignited on May 10 in what UN chief Antonio Guterres called "an alarming new chapter" in the conflict.
The overall conflict has killed tens of thousands, including up to 15,000 in a single West Darfur town, according to United Nations experts.