Sudan's President Omar al-Bashir, being sought to answer charges of war crimes, has asked for a US visa ahead of next week's UN General Assembly.
The International Criminal Court (ICC) wants Mr Bashir tried on charges of directing genocide and taking part in war crimes in the Darfur region.
State media had said Sudanese Foreign Minister Ali Karti would be leading the country's delegation to the meeting at UN headquarters in New York.
Mr Bashir last visited the US in 2006.
Warrants for his arrest were issued in March 2009 and July 2010. The ICC charged him with 10 counts of war crimes, crimes against humanity and genocide in connection with the conflict in the western region of Darfur.
The US ambassador to the United Nations, Samantha Power, confirmed that Washington had received a visa application from President Bashir. She described the move as "deplorable", "cynical" and "hugely inappropriate".
A spokeswoman for the US State Department, Marie Harf, said: "We condemn any potential effort by President Bashir to travel to New York."
"Before presenting himself to UN headquarters," Ms Harf said, "President Bashir should present himself to the ICC in The Hague to answer for the crimes of which he's been accused."
Ms Harf did not say whether Mr Bashir's visa application had been rejected.
The US has made legal commitments to grant visas to officials seeking to take part in activities of the UN, the Sudan Tribune newspaper reports.
One scenario is that the Sudanese leader could be arrested if he sets foot on US soil whilst en route to the UN headquarters. The site itself is regarded as extra-national territory, the AFP news agency reports.
Last month, Saudi Arabia refused permission for a plane carrying the Sudanese president to cross its airspace, as Mr Bashir travelled to Iran to see the inauguration of the new Iranian president.