Armed Forces Commander General Gatot Nurmantyo was preparing to board a flight to Washington on Saturday when he was told by the airline that the US Customs and Border Protection agency had denied him entry into the country.
The US embassy in Jakarta issued a statement saying it was in contact with Nurmantyo's staff and was attempting to facilitate his travel to the US, but didn't provide further details.
"We deeply regret the inconvenience that this incident caused and we apologise", McKee told reporters after meeting Foreign Minister Marsudi.
"With regard to the travel problems experienced by the TNI [Indonesian Military] chief, the Indonesian government should protest to the U.S. authorities rather than request clarification", Dino Patti Djalal, former ambassador to the United States, said in a tweet on Sunday.
The US deputy ambassador to Indonesia, Erin Elizabeth McKee, said the US government regretted and apologised for the incident and hoped it will not happen again.
"There is a sense of urgency to this that we have conveyed to them", she said, adding that USA officials were "trying to coordinate with relevant authorities in the U.S.to find out what really happened".
US Ambassador Joseph Donovan also offered an apology, according to a statement Sunday from the embassy.
WTA Finals: Top-ranked Simona Halep hoping to keep dream alive
Billie Jean King was 39 in 1983 and Martina Navratilova was 38 in 1994. She broke Williams again in the final game of the match. That's what I was trying to do today and it worked'.
Some Indonesians reacted indignantly to the incident, putting up banners around the capital calling for the U.S. ambassador to be expelled and for Americans to be "sent home".
Earlier in October, the United States embassy to Jakarta published a statement saying that Dunford had invited Nurmantyo to attend a Chiefs of Defense Conference on Countering Violent Extremism slated for October 23-24 in Washington.
However, Marsudi said Indonesia would continue asking the USA government for an explanation for the rejection.
Nurmantyo will not attend the conference unless this clarification is received, the military said.
Nurmantyo is a controversial figure in Indonesia because his actions and words frequently suggest he has political ambitions.
Indonesian President Joko Widodo said this month that the armed forces should stay out of politics and ensure their loyalty is only to the state and the government. But relations have sometimes been strained over American resource companies operating in Indonesia or alleged rights abuses involving Indonesia's military.