Libya's UN-backed unity government has said France had not coordinated with it over the presence of French troops in Libya and that it would not compromise on its sovereignty after France announced the deaths of three of its soldiers there.
Special forces teams from countries including France, Britain and the United States are on the ground in western and eastern Libya.
The French have been working alongside forces loyal to eastern Libyan commander Khalifa Haftar against Islamist militants. Haftar has rejected the UN-backed Government of National Accord (GNA) in Tripoli, which is backed by major Western powers including France.
The GNA's Presidential Council said in a statement released late on Wednesday that it had asked France for an explanation after President Francois Hollande announced the soldiers' deaths during "dangerous intelligence operations".
"The Presidential Council expresses its deep discontent at the French presence in eastern Libya without coordination with the Council, which was declared by the government of France," said the statement from the unity government.
There could be "no compromise" over Libyan sovereignty, the council said in the statement. It also said the council had contacted the French authorities demanding an explanation.
Hollande called the helicopter crash an accident, but an Islamist-led armed group fighting against forces loyal to Haftar claimed it had shot the helicopter down. A military spokesman from Haftar's forces in eastern Libya said the French had died when their helicopter came down south of Benghazi on Sunday.
Western powers are hoping the GNA can end the turmoil and conflict that developed after Libyan leader Muammar Gaddafi was toppled in an uprising five years ago.
They have said they are ready to help Libya tackle the threat from Islamic State, but the GNA says any assistance must follow its own request.