Some 200 people have been granted passage into Tunisia through the Ras Jedir border crossing, before Tunisian officials again closed the border after just a few hours, as heavy fighting rages in neighbouring Libya.
Tunisian citizens as well as foreign workers from Egypt and Libyans fleeing from the violence were allowed passage during a short period on Saturday, even as 10,000 to 15,000 remain stuck in the border, Al Jazeera's Ruli Amin, reporting from Ras Jedir, said.
Our correspondent said that the border crossing was "much more under control" compared to Friday, when hundreds of mostly Egyptians trying to leave clashed with Tunisian police.
"For many many who are still stranded in Syria, this is the only way out."
In places like this and in these kinds of situations there is a very small difference between things going well and going very, very badly
The Tunisian government on Friday urged its 50,000 to 80,000 nationals still in Libya to come home as quickly as possible, prompting large number of people to flock to the border.
But Tunisia also said it could not cope with taking in the many Arab and Asian people working in Libya as it did during the 2011 revolt.
Tunis will let through only foreigners whose governments guarantee immediate repatriation.
Egypt's ambassador in Tunis, Ayman Musharafa, announced on Saturday that Cairo would fly home from Tunisia those of its citizens who were allowed to enter the country.
A short time later, several dozen Egyptians carrying their possessions were allowed to enter Tunisia, where they boarded a bus to be taken to an airport.
"The government undertakes to evacuate on average from 2,000 to 2,500 people per day by air," Musharafa told reporters after meeting officials from both Tunisia and Libya.
Fighting rages on
On Saturday, the main fuel depot in the capital Tripoli has been set ablaze after rockets fired by one of Libya's armed groups struck and ignited a tank, the National Oil company (NOC) said.
Black plumes of smoke rose over the fuel tanks, which store oil for use in the capital and are located near Tripoli's international airport.
Firefighters deployed to tackle the blaze were forced back by the fighting, NOC spokesman Mohamed al-Harari said.
Meanwhile, Libya's newly elected parliament held an emergency meeting on Saturday to discuss the dire security situation threatening to tear the country apart.
The House of Representatives, elected in May, gathered in an attempt to set a political framework, and guide Libya out of the pit of violence that has raged for weeks in certain parts of the country. The assembly's first official session is scheduled for August 4.
"We want to speed up the handing over of process, because Libya cannot wait much longer," said Jalal al-Shwehdi, an MP said.
The ongoing violence has forced several countries to evacuate their diplomatic staff and citizens.
On Saturday, nearly 200 people from Greece, China and other countries arrived at a port near the Greek capital of Athens.
Passengers on the frigate Salamis described a deteriorating security situation in the Libyan capital Tripoli, with frequent power and water cuts.
Constantine Koutras, a spokesman for the Greek Foreign Ministry, said moving embassy staff to the port was the most difficult part of the operation.
"In places like this and in these kinds of situations there is a very small difference between things going well and going very, very badly," he said on state TV.
Britain says it will suspend work at its consulate in Tripoli once it has completed assisting the departure of British nationals.