Eastern groups say the region suffered from marginalization and unequal distribution of wealth under ousted dictator Moammar Gadhafi.
They demand the creation of a federal system in which each region has some autonomy, reviving the system in place from 1951 until 1963 when Libya, ruled by a monarchy, was divided into three states: Tripolitania in the west, Fezzan in the southwest and Cyrenaica in the east or Barqa, as it was called in Arabic.
During Wednesday's televised meeting, Essam al-Jehani of the Political Bureau of Barqa, one of the eastern groups, demanded the government hand power to a "federated council" where seats are allocated equally between Libya's three regions. A future system for the country would then be decided by a referendum.
The Tobruk meeting came after a 10-day ultimatum given last month by Zidan to the militia to open the terminals expired. The government however appeared to have no response ready for when the terms of the ultimatum were not met.
Zidan said during the new conference that he didn't want "bloodshed," but vowed, "the government will not stand with its hands tied forever."
The standoff over the terminals is one of many challenges to the central government. The country has no strong army or police, and has been struggling to control armed groups formed mainly of former anti-Gadhafi rebels. Some militias are driven by political agendas and alliances in parliament, while others are backed by certain cities, tribes or regions.
Last month, Washington said it is planning to train 5,000 to 8,000 Libyan soldiers in the continuing effort to improve security. A stronger army is seen as key to reining in the militias.
McCain reaffirmed the US pledge to train Libyan troops in his visit. "It (progress) can only been achieved by the cooperation of assistance of the United States and other friends in Europe and in the region," he said.
The senator meanwhile thanked Zidan and the Libyan government for their cooperation in the investigation of a 2012 attack on the U.S. consulate in Benghazi which killed Ambassador Chris Stevens as well as three other Americans, blamed on a hard-line militia.
Zidan said investigations would resume as soon as the security situation in Benghazi improved.
Benghazi continues to be hard hit by violence attributed to the armed groups. In the latest attack there, a hand grenade killed a senior officer when he was driving his car from the passport and citizenship department in the city center, a security official said.
Meanwhile, in the southern region of Sabha, unidentified gunmen looted a bank truck carrying nearly $2 million, another security official said. It was at least the third such bank truck robbery in less than two months.
All officials spoke anonymously for fear of retribution.
Libya has seen in the past weeks a popular backlash against militias in some places. Scores were killed when a militia opened fire last month during a march on their headquarters in Tripoli, triggering outrage. Since then, residents of other cities have also marched against the militias.
The eastern city of Darna, known as a stronghold of the hard-line Ansar al-Shariah, has seen a series of night matches against the militias in recent days.
Early Wednesday, a security official said that an explosion rocked the city center, killing local activist Murad al-Zawi and leaving his vehicle on fire.
