Renegade ex-general Khalifa Haftar said Saturday the Libyan people have given him a "mandate" to crush jihadist militants in the country, a day after thousands rallied in his support in Benghazi and Tripoli.

Haftar's campaign has won growing support amid frustration at the lawlessness in Libya three years after the overthrow of dictator Muammar Gaddafi.

"We have accepted the mandate of the people," Haftar said in a statement.

"The (people) have given their instructions ... We pledge not to abandon this mission until Libya is purged of terrorists and extremists and all those who back them," he added.

The statement was released by Haftar's self-declared "supreme military council" in the Benina region near the eastern city of Benghazi, where the rogue general launched his campaign this month.

Thousands of demonstrators rallied in support of Haftar on Friday in the capital Tripoli and in Benghazi, the cradle of the 2011 uprising against Gaddafi and hotbed of an Islamist militancy since.

The demonstrations were some of the largest seen in Libya since Gaddafi was toppled and killed in 2011.

On Wednesday, Haftar warned that Libya has become a "terrorist hub" and called for the formation of an emergency cabinet and legislative elections to be held.

His forces launched an assault against jihadists on May 16 in the Mediterranean city of Benghazi, in which at least 79 people were reported killed.

That prompted the government to brand him an outlaw and claim he was attempting a coup.

But Haftar insists he has no interest in power, just an end to the Islamist-dominated General National Congress, or interim parliament.

Also on Saturday the spokesman of Haftar's paramilitary "National Army", Mohammed al-Hijazi, called on troops to "rejoin" their units without elaborating.