It was unclear whether Thani planned to follow through on his vow, and a government spokesman said the premier had not stepped down.
Thani made the resignation promise during an emotional live television appearance in which he faced a barrage of angry questions from citizens.
The move added to the political chaos in Libya, as the country's rival factions met for a second day of UN-sponsored peace talks in Geneva.
Thani faced questions in yesterday's programme from Libyans blaming his government for the lack of basic services such as electricity and poor security in areas it controls.
Adding to the confusion, government spokesman Hatem el-Ouraybi said Thani's promise had been conditional.
"The prime minister said during the interview that he would resign if people wanted him to, that's it," Ouraybi told AFP.
He said no resignation letter had yet been submitted to parliament. "I don't now have an answer to the question of whether it will be submitted on Sunday."
Libya, which plunged into chaos after the ouster and killing of its leader Moamer Kadhafi in a 2011 revolution, has two rival governments and parliaments vying for power, as well as several militia groups battling for control of its oil wealth.
Thani's government has been working out of a small eastern city near the border with Egypt since an Islamist militia alliance captured the capital Tripoli last year.
The international community recognises the parliament that sits in the eastern port of Tobruk.
A partial peace deal aimed at restoring stability was reached last month, but leaders of the Islamist-backed General National Congress (GNC) parliament that sits in Tripoli boycotted the pact, calling it "unsatisfactory".
The rival factions started a new round of peace talks in Geneva yesterday, with representatives of the Tripoli parliament this time joining the meetings.
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