The State Department refused to say Wednesday whether it will allow Sudan’s longtime leader — indicted as a war criminal in the deaths of more than 200,000 people — to come to New York for next week’s annual meeting of the U.N. General Assembly.

“We have an obligation as host nation for the U.N.,” State Department spokeswoman Marie Harf said, referring to the general practice of allowing foreign leaders and diplomats entry to the United States for U.N. business. “I’m just not going to speculate what action we may or may not take other than to say we act consistent with our relevant international obligation.”

U.N. Ambassador Samantha Power started a diplomatic shoving match Monday when she said the United States had received a request for an entry visa from Sudanese President Omar Hassan al-Bashir. It would be “deplorable, cynical and hugely inappropriate” for Bashir to attend the U.N. gathering, Power said.

“It would be more appropriate for him to present himself to the ICC and travel to The Hague,” Power said, referring to the International Criminal Court in the Netherlands. Bashir faces 10 counts of war ­crimes, ­crimes against humanity and genocide but has refused to surrender for trial.

“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,” Harf had said Monday.

Bashir is charged with crimes arising from the years-long conflict in the western Darfur region of Sudan.

Sudan denounced the United States on Wednesday for suggesting that Bashir should not attend the U.N. gathering.

The United States is not qualified “to offer sermons and advice” on human rights or international law, Sudan’s Foreign Ministry said, in particular because Washington is not a member of the international court and considers itself independent of the court’s decisions. Bashir should be quickly granted a visa to visit New York, the government in Khartoum said.

Harf said she had not seen the Sudanese critique.

The United States, as the host country for the world body, is obligated to grant entry visas for leaders it considers illegitimate or worse. Iranian and Cuban leaders regularly receive entry visas for the U.N. gathering, as has Zimbabwe’s President Robert Mugabe.

Bashir’s case is somewhat different, as he is the first sitting head of state indicted by the international court. He has traveled abroad only rarely since the indictments in 2009 and 2010, and his application to come to New York this year apparently took U.S. officials by surprise. He last visited the United States in 2006.

Privacy laws prevent the State Department from commenting in detail about individual visa applications, Harf said.

“We confirm that he’s put in a request. I’m not just going to probably go any further today,” Harf said. “As host nation of the United Nations, we are generally — I’m not speaking in this case specifically, but generally — obligated to admit foreign nationals traveling to U.N. headquarters for official U.N. business.”