"Armed men have besieged the congress, but we do not know the motive of the attack," Tahar Mokni told AFP.
"We suspended our proceedings, and the vote has been postponed until next week," he added, with witnesses saying MPs had been evacuated from the building as shots continued to be heard.
The GNC, the country's highest political authority, had been preparing to hold a second vote between two candidates to replace Abdallah al-Thani, who stepped down over security fears less than a week after being appointed earlier this month.
University professor Omar al-Hassi, from the restive eastern city of Benghazi, was second, with 34 votes.
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Some MPs said the attack was carried out by partisans of one of the two men after rumours began circulating that he would lose the vote.
A number of deputies, doubtful that either candidate would obtain the 120 votes required for election, proposed putting off the poll until a consensus candidate could be found.
Libya's weak central government has struggled to rein in heavily armed former rebel brigades from the 2011 uprising that ended Moamer Kadhafi's four-decade rule, many of which have carved out their own fiefdoms and refused to join the security forces.