Soldiers stormed the national radio headquarters in Libreville, Gabon's capital, stating they were disappointed with Bongo's message for the New Year.
A fifth officer fled and is being searched for, he said.
Four of five Gabon military officers who attempted a coup in the early hours of Monday morning have been arrested at the radio station they briefly took control of, government spokesman Guy-Bertrand Mapangou told Reuters.
The leader of a rebel military group which staged a foiled coup in Gabon has been arrested and two of his commandos killed.
Gabonese President Ali Bongo Ondimba gestures as he speaks to journalists during an interview in Libreville, on August 12, 2016.
"The secretary-general does take note that calm appears to have returned to Libreville and calls on all actors to follow the constitution", Dujarric said.
"His special representative for Central Africa Francois Lounceny Fall is monitoring the events closely and is ready to provide good offices if and as required", the spokesman said. His family has ruled the oil-rich Central African nation for almost half a century.
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The military in Gabon has seized power in oil-rich West African country, where the ailing Ali Bongo's family has ruled for 50 years.
Bongo had acknowledged health problems in his New Year speech but said that he was recovering.
In the White House's letter to House Speaker Nancy Pelosi regarding deployment in Gabon, President Donald Trump wrote troops "will remain in the region until the security situation in the Democratic Republic of the Congo becomes such that their presence is no longer needed".
Bongo became ill in October while on a visit to Saudi Arabia.
It was revealed last month that he had suffered a stroke.
Gabon is now being run by the prime minister and vice president after the Constitutional Court transferred some of the president's power in his absence.
In a message on state radio, military officers declared their dissatisfaction with Bongo, who is recovering from a stroke in Morocco. In 2016, during his re-election, violent protests broke out amid claims of fraud.