General Gatot - who earlier this year suspended military ties with Australia over teaching materials perceived as derogatory at a Perth Army base - was travelling to Washington with his wife and a delegation.

He had been invited to attend a conference on countering violent extremism on October 23 to 24 at the invitation of General Joseph Dunford, the US's highest ranking military officer.

However, the Indonesian Armed Forces said moments before General Gatot's departure on Emirates, the airline informed him he had been denied entry to the United States by US Customs and Border Protection despite having a visa.

Indonesian Foreign Ministry spokesman Arrmanatha Nasir said the Indonesian Embassy in Washington DC had sent a diplomatic note to the US Foreign Ministry to obtain clarification on what had happened.

"Considering the US Ambassador is out of Jakarta at the moment, the Deputy Ambassador has been summoned to Kemlu (the Foreign Ministry) tomorrow to give an explanation," Mr Nasir said.

TNI (Indonesian Armed Forces) spokesman Wuryanto said General Gatot had been invited to attend a conference on countering violent extremism by his "best friend and senior" General Joseph Dunford, the Chairman of the Joint Chiefs of Staff.

"Based on the invitation, the Indonesian Military Commander responded and confirmed his attendance as a form of respect to the party who invited him," Mr Wuryanto said.

"His visa and all administrative matters had been taken care of and there was no problem."

Mr Wuryanto said after being denied entry General Gatot reported what had happened to the President, Foreign Minister and Chief Security Minister.

"The Indonesian Military Commander has also sent a letter to the US Military Commander," he said.

"The TNI is still waiting for an explanation for this incident considering the travel to the US was upon an invitation from the US Military Commander and upon a good relationship between the two countries."

He said General Gatot, his wife and delegation had decided not to attend the conference until there was further information from the US.

The US Embassy in Jakarta issued a statement saying General Gatot was "unable to travel as planned".

"US Ambassador Joseph Donovan has apologized to Foreign Minister Retno Marsudi for any inconvenience to General Gatot," it said.

"The Embassy was in touch with the General's staff about this matter throughout the weekend, working to facilitate his travel.

"The US Embassy was, and remains, prepared to facilitate the General's travel to the United States. We remain committed to our Strategic Partnership with Indonesia as a way to deliver security and prosperity to both our nations and peoples."

Former Indonesian Ambassador to the US Dr Dino Patti Djalal tweeted that the Indonesian government should be conveying its protest to the US not asking for clarification.

Lowy Institute Research Fellow Aaron Connelly said it appeared to be an "administrative SNAFU" given General Gatot had been invited to attend the conference.

"If there were a substantive issue preventing his entry into the United States, then he wouldn't have been invited," Mr Connelly said.

"But because Gatot has built his reputation on identifying phantom threats to Indonesian sovereignty and pride, a slight like this can only boost his standing among Indonesians in a nationalist mood."

General Gatot had previously raised concerns about the US Marines that rotate through Darwin, pointing out the close proximity to West Papua and Indonesia's giant Masela gas block.

"I, as TNI Commander, have to wonder what it's all about," General Gatot said in a lecture. "Why not in the Philippines? They have a base there. No problems, but it's Darwin."

He also spoke of putting a stop to Australia trying to recruit Indonesian officers as spies or agents of influence.

"In public speeches he often espouses his pet theory that foreigners are engaged in a proxy war to undermine Indonesia," author and Indonesia commentator John McBeth wrote in Asia Times this month.

President Joko Widodo named General Gatot, the former army chief, to the position of Indonesian National Armed Forces chief on July 8, 2015.

Evan Laksmana, a senior researcher with the Centre for Strategic and International Studies (CSIS) in Jakarta, tweeted that entry refusal was a very serious matter for bilateral relations.

He said he was sceptical it was related to typical alleged human rights abuses because the entry refusal was last minute and General Gatot had entered the US before.

Mr Laksmana tweeted that typical refusal of entry was related to military operations and career, as several TNI officers had experienced in the past.

"But not sure how this applies to Gatot. Like most he did have operations in Timor but I can't remember his name coming up in investigations over that period or lately."

General Gatot, who is believed to have political aspirations when he retires from the military in March next year, stirred controversy last month when he alleged a number of non-military institutions had ordered 5000 illegal firearms from overseas.

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