The clashes in Nasir, near the Ethiopian border, between national forces and the White Army, a loosely organised group mostly comprising armed ethnic Nuer youths, had threatened to reignite the 2013-2018 civil war in which hundreds of thousands of people died.
The government accuses the party of First Vice President Riek Machar, a Nuer, of collaborating with the White Army, which fought alongside Machar's forces during the civil war against the predominantly ethnic Dinka troops loyal to President Salva Kiir. Machar's party has denied involvement.
A South Sudanese general was among around 27 soldiers killed on March 7 when a UN helicopter trying to evacuate them from Nasir came under attack.
South Sudan's Information Minister Michael Makuei told journalists at a news conference the airforce bombed Nasir on Monday morning.
Kang Wan, a community leader in Nasir, said it happened late on Sunday night, and that of the 19 dead, 15 people were killed immediately, while the others later succumbed to their wounds. Another resident said they saw 16 bodies and that three others had died.
"All of them they got burned, everything got burned," Wan told Reuters by telephone.
Medecins Sans Frontieres said its hospital in nearby Ulang received three wounded patients from Nasir on Monday morning.
"Two of them were declared dead on arrival due to the severe burns they had sustained," MSF said in a statement, giving no further details.
Nasir County Commissioner James Gatluak Lew, who is allied to Machar, said the South Sudanese armed forces were likely seeking revenge for the helicopter attack.
Last week Uganda said it had deployed special forces in South Sudan's capital Juba to "secure it". The South Sudanese government at the time denied the presence of Ugandan troops in the country.
However, Makuei said in a statement some Ugandan army units were in the country "to back up and support the (national army) according to their needs".
