"I reaffirm the AU's total rejection of all unconstitutional change of power", he wrote on Twitter.
They took control of the national radio station at 03:30 GMT to read a short statement announcing a "National Restoration Council".
In his first public statement since falling ill, he issued a New Year's address from the Moroccan capital Rabat acknowledging he had been "through a hard period" and promised to return soon.
Four hours later, a spokesman for Gabon's government called the soldiers "mutineers" and "jokers" and said four out of five of them have been arrested.
"Two of the coup participants were killed when security forces took over and freed some hostages, according to a presidential statement reported by RFI [Radio France International]", the Associated Press (AP) reports.
In the message he gave to the nation on December 31, he expressed gladness that the condition of his health was improving.
Obiang said President Ali Bongo - who has been out of the country for over two months - can not fulfil his responsibilities. However, AP notes that the government has imposed a curfew over the capital and has cut the cord on the internet.
Tanks and armed vehicles could be seen in the capital Libreville.
Several hundred people gathered in the streets near the radio headquarters, with some cheering for the coup leaders, but they were reportedly dispersed with gunshots and tear gas fired by army loyalists.
The Gabon Military has overthrown the government after claiming that President Ali bongo and his family had ruled the country for the past 50 years. His family has ruled the oil-rich country for over half a century.
Bongo won re-election in 2016 by fewer than 6,000 votes, sparking deadly clashes between protesters and police during which the parliament was torched.
Mr Bongo's father, Omar, was president for 42 years before he died in 2009 and was replaced by his son. The president has been out of the country since October amid reports he had a stroke.