There are reports of heavy weapons being fired near a military headquarters just outside Juba.
Several thousand people have taken refuge at two United Nations compounds.
On Monday, President Salva Kiir blamed soldiers loyal to his dismissed former deputy Riek Machar for the violence, but said the government was in control.
He said the violence first broke out on Sunday night after unidentified uniformed personnel opened fire at a meeting of the ruling party, former rebel force the Sudan People’s Liberation Movement (SPLM).
A night time curfew is now in place and at least four former ministers have reportedly been arrested following the alleged coup. Mr Machar’s whereabouts are unclear.
President Kiir sacked Mr Machar, along with his whole cabinet, in July. The sackings are believed to have followed a power struggle.
Mr Machar, who has said he plans to contest the presidential elections in 2015, now leads a dissident faction within the SPLM.
On Tuesday, South Sudan’s Foreign Minister Barnaba Marial Benjamin said there was renewed fighting in Juba as the military “cleared out remnants” of Mr Machar’s alleged supporters.
The US special envoy to the country, Donald Booth, told the BBC the airport was closed and telephone connections had been severely curtailed.
At least 12 people are reported to have been killed. The government said some 120 people had been taken to a hospital for treatment.
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.
But the oil-rich country remains ethnically and politically divided, with many armed groups active.