The militias, known as Libya Central Shield, are composed of groups from the western city of Misrata. They are under the command of the country's chief of staff, who answers to parliament. The Islamist-dominated legislature has described the campaign by Gen. Khalifa Hifter as a coup.
Witnesses in Tripoli said they saw Misrata militiamen take positions early on Thursday in army barracks in the city's south, near the airport highway. The residents spoke on condition of anonymity, fearing for their own safety.
The parliament - challenged by its own government, which is pressing for a suspension of the house's sessions until new elections - has called in the forces to face off pro-Hifter militias in the capital.
No fighting was reported on Thursday but dozens of people have been killed since Hifter's offensive began last Friday, first in the eastern city of Benghazi and then, two days later, with the storming and ransacking of parliament by militias allied to Hifter, who declared the body suspended.
On Wednesday, Hifter called for the formation of a Presidential Council to take over from parliament, oversee elections and hand power after a nationwide vote to a new legislature.
Hifter has also been winning support from several prominent government officials and military units for his campaign against Islamists whom he accuses of tearing the country apart and orchestrating militant attacks with the support of Libya's Islamist-dominated parliament.
Hifter's offensive has plunged Libya deeper into instability.
Following the eight-month civil war in 2011 that toppled and killed longtime dictator Moammar Gadhafi, the North African oil-rich nation of nearly six million people descended into lawlessness.
The conflict left the country without a regular army or a strong police force. Rebels who fought Gadhafi later formed armed militias that turned Libya into fiefdoms and put pressure on the elected government.
Daily assassinations, kidnappings and lootings - more frequent on the eastern half of the country and the heartland of the rebel movement - and out-of-control militias have further undermined the government's efforts to achieve stability.
The government also appears split between Islamists who have denounced Hifter's offensive and those who back him.
Some army troops, Libya's air force and the navy have joined Hifter's self-styled "Libyan National Army," though it's not clear how deep the split is among the military.
The latest to side with Hifter was Culture Minister al-Habib al-Ameen, who has also acted as a government speaker.
He urged Libyans in several TV interviews late Wednesday to "rescue the last breath" of the country.