In a meeting on Friday, the pro-Syrian factions "once again unanimously confirmed their rejection of giving up the principle of forming a government under his leadership," said Parliament Speaker Nabih Birri, one of Syria's closest allies.
The Lebanese political process has been deadlocked for weeks since Karami stepped down in the wake of former premier Rafiq al-Hariri's assassination in a bomb blast on 14 February.
Karami later resumed the post but said earlier this week that he was relinquishing efforts to form a Cabinet because of objections from the opposition.
The impasse threatens to delay parliamentary elections, which must be held before 31 May, the day the current legislature's mandate expires.
Karami's failed effort to form a Cabinet prompted criticism from opposition member of parliament Bahiya al-Hariri.
"This is an attempt to extend the parliament, a move I think is a declaration by the government of its lack of confidence to form the next one," she said on Friday, Aljazeera reported.
Also on Friday, a prominent Christian politician said the anti-Syrian opposition would win a majority in parliamentary elections whether they were held on time in May or delayed.
The opposition has accused Syria and its Lebanese allies of seeking a postponement to avoid likely defeat in the polls and to prolong the life of the mainly pro-Syrian parliament.
"I think that even a technical delay is the first step to destroying the parliamentary democratic system that we have in Lebanon"
Maronite Christian MP
"We are putting up a fight in order to avoid any delay, and I think that even a technical delay is the first step to destroying the parliamentary democratic system that we have in Lebanon," said Maronite Christian MP Boutros Harb.
But even if those efforts failed, he said he was confident of victory for the opposition that includes several religious groups and some former foes in the 1975-1990 civil war.
"They (the authorities) are betting on the time factor, that maybe in a few months things will be different... I personally think that it (the opposition vote) will increase," he said.