Islamist hardliners bulldozed part of a revered mausoleum in Tripoli on Saturday in the second such attack in Libya in two days, an AFP correspondent reported.
Deputy Prime Minister Mustafa Abu Shagur, in remarks on Twitter, condemned the actions as "crimes" for which which the culprits should be held responsible.
He had asked the defence and interior ministries on Friday to intervene "but they have not carried out their duty in protecting these sites."
The radicals used an excavator to demolish part of the mausoleum of Al-Shaab Al-Dahman, close to the centre of the Libyan capital, the correspondent said.
It was the second such assault on a Muslim pilgrimage site in as many days.
On Friday, hardliners blew up the mausoleum of Sheikh Abdessalem al-Asmar in Zliten, 160 kilometres (100 miles) east of Tripoli, a town which was rocked by deadly clashes earlier this week.
A video posted on social networking sites purported to show the building being blown up to cries of "Allahu Akbar (God is greatest)."
Witnesses told AFP on Saturday that another mausoleum, that of Sheikh Ahmed al-Zarruq, had been destroyed in the port of Misrata 200 kilometres (125 miles) east of Tripoli.
Hardline Sunni Islamists are implacably opposed to the veneration of tombs of revered Muslim figures, saying that such devotion should be reserved for God alone.
There are conflicting reports as to what triggered this week's clashes in Zliten, with some saying they were the result of a tribal vendetta and others that they pitted Islamists bent on destroying the shrine against other residents seeking to protect it.
The violence, which left at least three people dead and scores wounded, is on the agenda of the ruling national congress, which has requested a security briefing from the interior minister.
The national assembly's speaker, Mohamed al-Megarief, in a televised speech on Saturday, denounced "the destruction and pillage of several buildings" and historic manuscripts.
He also said it was "regrettable and suspect" that members of the security forces and former rebels may have taken part in the attacks.
"Such acts are rejected and illegal under the law and sharia (Islamic law)," Megarief said.
He added that the prime minister and defence and interior ministers, along with the intelligence chief and security service officials, have been called to appear before the assembly on Sunday to answer deputies' questions.
On Thursday, the national assembly, which was elected in July, met in closed session to discuss security problems across the country, with Interior Minister Fawzi Abdelali reportedly coming in for heavy criticism.
The session followed a double car bombing in Tripoli on August 19 that killed two people. Tribal clashes in the western region of Zliten have since left at least two dead and several wounded.
Rumours have been circulating in Tripoli for days that Abdelali and Defence Minister Osama Juili could both face the sack.