The United Nations said the incident, which could deal a blow to an already fragile peace process, was "utterly abhorrent" and a possible war crime.
The UN crew was trying to airlift soldiers following heavy clashes in Nasir between government forces and the White Army militia, a group which President Salva Kiir's government has linked to forces loyal to his rival and First Vice President Riek Machar.
In a address announcing the deaths of General Majur Dak and other soldiers, Kiir said Machar had assured him and the UN representative that the general would be safe and that the rescue mission should fly to Nasir to move him and his men.
Information Minister Michael Makuei told reporters that "approximately 27" troops were killed.
A UN crew member was among the dead.
It was not immediately clear if the helicopter was hit as it was in the air or if the attack took place while it was still on the ground.
Machar's spokesman Puok Both Baluang declined to comment on the attack.
Machar's party has previously denied involvement in the recent fighting in Nasir.
The head of the UN Mission in South Sudan (UNMISS), Nicholas Haysom, said the attack was "utterly abhorrent" and may constitute a war crime under international law.
"We also regret the killing of those that we were attempting to extract, particularly when assurances of safe passage had been received. UNMISS urges an investigation to determine those responsible and hold them accountable," he said.
Machar's spokesman said earlier this week that security forces had arrested the petroleum minister, the peacebuilding minister, the deputy head of the army and other senior military officials allied with Machar, potentially jeopardising the 2018 peace deal which ended a civil war between Kiir's and Machar's forces.
The government has not commented on the detentions and all the detained officials, apart from the peacebuilding minister, remain in custody or under house arrest, according to Machar's spokesman.
The White Army, which mostly comprises armed youth from the Nuer ethnic group, fought alongside Machar's forces in the 2013-2018 civil war that pitted them against predominantly ethnic Dinka troops loyal to Kiir.
Kiir on Friday reiterated that the country would not return to war but analysts have warned that the escalating tensions could lead to a full-blown conflict.
The UN in a statement urged "all actors to refrain from further violence and for the country's leaders to urgently intervene to resolve tensions through dialogue and ensure that the security situation in Nasir, and more broadly, does not deteriorate".
South Sudan has formally been at peace since the 2018 agreement ended the five-year war that killed an estimated 400,000 people but clashes between rival communities break out frequently.
The UN mission in South Sudan was established soon after the country won independence from Sudan in 2011.
Almost 20,000 peacekeepers from 73 countries serve in it.
