The US State Department said earlier this week that Washington received a visa request for al-Bashir, but that before going to the UN headquarters he should present himself to the ICC to answer for alleged crimes linked to the conflict in Sudan's Darfur.
An estimated 300,000 people have died since 2003 due to the fighting between the government and rebels in the western region.
"We condemn any potential effort by President Bashir to travel to New York, given that he stands accused of genocide, war crimes, and crimes against humanity by the International Criminal Court," said State Department spokeswoman Marie Harf. Sudan's Foreign Ministry said the United States is "not qualified ... To offer sermons and advice" on international law and human rights. Sudan's statement also criticised US support for Israel, and called on Washington to swiftly grant al-Bashir a visa.
Even though the US has welcomed al-Bashir's indictment by the ICC and will not allow its officials to meet with him, it has obligations as the host country of the United Nations to grant visas to foreign heads of state and government. It could deny the visa on other grounds, but that would risk running afoul of its UN obligations.
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Judges at the ICC made it clear Wednesday what they want Washington to do if al-Bashir visits New York.
While the US is not a member of the court, the judges stressed that the UN Security Council referred the Darfur case to the ICC and at the same time urged all countries to cooperate fully with the court.
Human Rights Watch said UN member countries should publicly oppose attendance by al-Bashir and make clear that if he does visit, they will not have any dealings with him nor take part in any events in which he is participating.