Bashir is wanted by the International Criminal Court on five counts of crimes against humanity and two counts of war crimes for atrocities allegedly committed in Darfur.
The rights group said Wednesday it was calling on world leaders to shun Bashir if he visits the United States to attend the general debate for the U.N. General Assembly, which starts Tuesday.
"If Bashir turns up at the U.N. General Assembly, it will be a brazen challenge to Security Council efforts to promote justice for crimes in Darfur," Elise Keppler, associate international justice program director at Human Rights Watch, said in a statement.
U.S. Ambassador to the United Nations Samantha Power said Tuesday a visit by the Sudanese president would be "inappropriate."
Sudanese Foreign Ministry spokesman Abu-Bakr al-Sideeg was quoted by the independent Sudan Tribune as saying the U.S. government had double standards when it came to war crimes.
The last of the U.S. war crimes came when it invaded Iraq under false pretenses, he said.
"The U.S. government is also the protector and supporter of the biggest violator of human rights and [worst] perpetrator of crimes against humanity and war crimes ... which is Israel," he added.
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