"We call on the government of South Sudan to carry out the necessary investigation, punish the guilty and take every measure to guarantee that this never happens again," the foreign ministry said in a statement on its website after Friday's incident.
A South Sudan military spokesman said troops fired anti-aircraft guns at the Russian Mil Mi-8 believing it was a rebel helicopter carrying weapons to anti-government forces in the world`s newest country.
"The tragic event in this African country raises with new urgency the question of the security of UN peacekeeping missions," it said, attributing the helicopter downing to "blunders."
"The governments of countries that accept missions and carry the main responsibility for the security of UN peacekeepers must approach this problem with all seriousness and recognise all the possible consequences of blunders," it said.
It named the men who died as S Ilyin, the pilot, A Abrarov, the second pilot, S Yegorov, the flight engineer, and N Shpanov, the cabin attendant and radio operator.
UN leader Ban Ki-moon had reacted furiously to the attack by the South Sudan army which brought down the peacekeepers' helicopter in the Likuangole district of the eastern Jonglei state.
He said it was a "clearly marked" UN aircraft and demanded that those responsible be brought to account. The UN Security Council and US government both deplored South Sudan's action.
The European Union's foreign policy chief Catherine Ashton also said in a statement Saturday that she "deplores" the attack and "calls on the government of South Sudan to give full cooperation in the investigation of this very serious incident."
Jongeli state has been stricken by ethnic strife since South Sudan became independent from Khartoum in July last year, becoming a base for rebellion against the new government.
It was a frontline state in four decades of near continuous civil war between South Sudan and the Khartoum government up to 2005 that left at least two million people dead.
Likuangole itself been at the centre of battles between rival tribes that have left thousands of people dead over the past year.