The Libyan capital has been controlled by dozens of militias with shifting loyalties and territories since the overthrow of dictator Moamer Kadhafi in 2011.
On Thursday, Mahmud Zagal, a militia commander from Misrata, announced the creation of the "Libyan National Guard", saying it would stay out of "political, party and tribal disputes".
It aims to continue the fight against the Islamic State jihadist group, secure state institutions and diplomatic missions, he said in a statement.
A GNA source said today that most of the groups involved had taken part in a seven-month battle to oust IS from its stronghold of Sirte, which fell in December.
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Misrata's well-armed militias, which control much of western Libya, led the fight but say the GNA stopped supporting them after Sirte fell.
"They now feel marginalised and are looking for support," the source said, asking to remain anonymous.
Misrata's powerful militias, which led the fight, control much of western Libya.
Several locals said the militias included backers of Khalifa Ghweil, the leader of a self-proclaimed "Government of National Salvation" which in January tried and failed to seize three government ministries in the Libyan capital.
The United States said yesterday it had noted with "serious concern reports that numerous tactical vehicles from an organisation claiming to be the 'Libyan National Guard' have entered Tripoli".
"This deployment has the potential to further destabilise the already fragile security situation in Tripoli," it said.
It said Libya should work to build "a unified national military force under civilian command that is capable of providing security for all Libyans and combating terrorist groups."
It also weakens the GNA, which has been unable to establish its authority despite its efforts to create a "Presidential Guard" to secure state institutions and diplomatic missions.
Formed in March last year, the unity government faces hostility from a rival authority based in the east of the country, which refuses to recognise its authority.