Salva Kiir said the government was in full control of the capital, Juba, after a night of heavy fighting between soldiers in the presidential guard.
A night time curfew has been put in place and a number of arrests have reportedly been made.
Several people were reported injured and hundreds have fled to a US base.
Hilde Johnson, the UN’s special representative in South Sudan, said she was “deeply concerned” and urged “all parties in the fighting to cease hostilities immediately and exercise restraint”.
“I have been in touch regularly with the key leaders, including at the highest levels to call for calm,” she said.
The fighting in Juba broke out overnight, and intensified in the early morning, with reports of continuous gunfire and several explosions.
The city’s airport has been closed and the state TV channel SSTV went off air for several hours.
Shortly after it came back on air, SSTV broadcast an address from Salva Kiir, wearing military uniform rather than his usual civilian clothing and flanked by government officials.
He said the violence “was an attempted coup”, but that the government was now in full control and the attackers were being chased down.
Salva Kiir said the fighting began when unidentified uniformed personnel opened fire at a meeting of SPLM, followed by an attack on army headquarters near the university carried out “by a group of soldiers allied to the former vice-president Dr. Riek Machar and his group”.
“I will not allow or tolerate such incidents once again in our new nation. I strongly condemn these criminal actions in the strongest terms possible,” the president said, vowing those responsible would be have to stand “before the appropriate law institution”.
The ruling party, former rebel force the Sudan People’s Liberation Movement (SPLM), would never allow power to be transferred by force, he said.
He announced a curfew would be in place every night between 18:00 and 06:00, beginning on Monday.
“Rest assured that the government is doing all it can to make sure that citizens are secured and safe.”
Foreign Minister Barnaba Marial Benjamin told the Associated Press that some soldiers had tried to raid the weapons store at the main military based in the capital, but were repulsed.
He said some politician had since been arrested.
Riek Machar has not commented and his whereabouts are unclear. But his spokesman said he was safe and denied reports he had been arrested.
South Sudan – the world’s youngest country and one of the least developed – has struggled to achieve a stable government since becoming independent from Sudan in 2011. The independence referendum was intended to end a decades-long conflict, led by the SPLM, against the north.
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