Constant gunfire and explosions in the early morning were followed by a few hours of relatively calm before sporadic gunfire restarted, witnesses said.
Donald Booth, the U.S. special envoy to Sudan and South Sudan, told the BBC: "The situation remains clearly tense and unsettled."
The fighting has killed at least 26 people and exposed deep ethnic rifts in Africa's youngest nation, which ceded from Sudan two years ago.
President Salva Kiir said on Monday the fighting between army factions was a bid to seize power by the former vice president, Riek Machar, whom he sacked in July.
The two men, from opposing ethnic groups which have clashed in the past, have long been political rivals. Analysts said divisions run deeper and rivalries in army ranks have long simmered.
Poor communications in Juba, where the mobile phone system has not operated since Monday evening, meant it was difficult to obtain a broad picture of the number of dead during the clashes, which have involved heavy arms and artillery.
Makur Matur Kariom, a doctor and health ministry official, told that at least 26 people had died among the casualties brought to Juba Teaching Hospital, where he has been treating many wounded.
Residents near Juba airport, which has been closed since Monday, were woken before dawn by gunshots and blasts, a U.N. worker said. Others also reported bouts of shooting.
It is unclear whether those who died were fighting for or against the government.
A night-time curfew is in place, and at least four former ministers have been arrested since Sunday's alleged coup.
The government said it was looking for Machar who had gone into hiding.
South Sudan is facing its biggest challenge since becoming independent.
By Ruchi Singh
reporter
Park Sae-jin
swatchsjp@ajunews.com