"This is a hostile act, direct interference and amounts to a declaration of war," the GNA said in a statement.
The war of words came on the eve of a virtual meeting of Arab League foreign ministers on Libya, in which the GNA declined to participate. That meeting, which had originally been scheduled for Monday, has been pushed back to Tuesday.
On Saturday, Egyptian President Abdel Fattah Al Sisi warned that if pro-GNA forces advanced on the strategic city of Sirte — some 450 kilometres east of Tripoli — it could provoke a "direct" intervention by Cairo.
For the Libyan state, "interference in its internal affairs, attacks on its sovereignty, whether by declarations... like those of the Egyptian president or by support for putschists, militias and mercenaries, is unacceptable," the GNA said.
The GNA called on the international community to "assume its responsibilities with regard to this escalation".
It said it was open to "all impartial mediation... under the aegis of the UN" but rejected "unilateral or extrajudicial initiatives".
Oil-rich Libya has been torn by violence, drawing in tribal militias, extremists and mercenaries since the 2011 toppling and killing of longtime dictator Muammar Qadhafi in a Western-backed uprising.
Since 2015, a power struggle has pitted the Tripoli-based GNA against strongman Khalifa Haftar, who claims legitimacy from an eastern-based elected parliament.
Haftar has been trying unsuccessfully to seize the capital since April 2019, with support from neighbouring Egypt, Russia and the United Arab Emirates.
Since the start of June, increased Turkish support has enabled pro-GNA forces to take control of northwest Libya, ending Haftar's assault on Tripoli.
The GNA advance is now halted outside the coastal city of Sirte, a strategic access point to Libya’s key oil fields which remains under Haftar’s control.
Sirte and Al Jufra to the south represents a "red line”, Sisi said in a television broadcast on Saturday, citing the need to protect Egypt’s porous border.
If this line is crossed, Egyptian forces will directly intervene in Libya, Sisi said.
"All of Libya is a red line,” the GNA responded. "Whatever the dispute between Libyans, we will not allow our people to be insulted or threatened.”
But the speaker of Libya’s eastern-based parliament Aguila Saleh defended Sisi’s declaration, saying in a Sunday statement that the Egyptian president was "responding to our appeal to the Egyptian parliament” last January in which Saleh called for Egyptian intervention in Libya.