The UN says that the war in Darfur that began in 2003 has killed about 300,000 people. Khartoum disputes the figure and says only 10,000 people have died in the conflict.
The unrest was triggered by a rebellion started by Darfuris who accuse the government of marginalising them.
Speaking in Khartoum, the Sudanese capital, Kerry said: "It's a pleasure for me to be here in Sudan and I look forward to some very in-depth discussions.
"There are obviously some very, very important issues for us to talk about."
Kerry said he would "engage on humanitarian issues and obviously issues pertaining to the conflict".
"We are very hopeful that we can make progress" he said.
Washington's overtures are seen as a softening of its stance on al-Bashir who expelled Western aid agencies after the ICC indicted him for war crimes and crimes against humanity in March.
Hillary Clinton, the US secretary of state, said shortly after the expulsion that al-Bashir would be held responsible for "every single death" in the places where the agencies had operated from.
Ali Sadiq, a foreign ministry spokesman, said Kerry's visit is a "a clear manifestation of the [attitude] of the Obama administration towards Sudan".
Relations between the US and Khartoum have been strained for many years, particularly after the US imposed sanctions on Sudan in 1997 for harbouring Osama bin Laden, the leader of al-Qaeda.
It also bombed a pharmaceutical plant in Sudan a year later, saying the site was used to make chemical weapons.