“Even if it was stupid, there’s significantly more political upset in Gabon then there has been,” said Eric Benjaminson, a former United States ambassador to the country, who left in 2013. “It’s a marker for something.”

“Mr. Bongo needs to return to Gabon,” he said, “and do something positive for the country.”

In a New Year’s Eve speech broadcast from Morocco, where Mr. Bongo, 59, was recuperating, the president sought to reassure the nation that he was fit.

“It is true that I have been through a difficult period, as sometimes happens in life,” he said. “Today, as you can see, I am better and I am preparing to meet you again soon.”

Observers noted that the president had slurred some words and did not move his right arm.

The first indication that something was amiss in Libreville on Monday came early in the morning, when songs from the campaign of Jean Ping, Mr. Bongo’s chief opponent in the 2016 presidential election, were broadcast over national radio.

A call to the station during the broadcast was answered by Lt. Kelly Ondo Obiang, the leader of the self-declared Patriotic Movement of the Defense and Security Forces of Gabon, who said he would announce a coup shortly. He went on the air and did just that, while station employees were held hostage during the broadcast.

Lieutenant Obiang said that Mr. Bongo’s speech from afar had “reinforced doubts about the president’s ability to continue to carry out of the responsibilities of his office.”