Anti-government protesters plan a third day of protests as they have clashed with police over the failure to remove uncollected rubbish from the streets.
Police used water cannon and tear gas to try to disperse the crowds and dozens were injured.
Lebanon does not have a president and parliament remains in a stalemate.
Tammam Salam’s unity government has been accused of being hamstrung by sectarian rivalries exacerbated by the conflict in neighboring Syria.
Unrest has been building because of the government’s failure to clear up rubbish piled on the streets of Beirut since the country’s biggest landfill closed last month.
They blame political paralysis and corruption for the failure to resolve the crisis.
On August 23, protesters threw rocks and sticks at police and lit fires.
If Tammam Salam were to resign it could trigger a constitutional crisis because in Lebanon the prime minister is appointed by the president, but the presidency has been vacant for over a year.
Replacing the president requires a deal many say can only be brokered by Iran and Saudi Arabia.
Tammam Salam said that if a cabinet meeting later in the week failed to resolve the waste issue, Lebanon’s heavily-indebted government was in any case likely to collapse.
The prime minister had already warned that the heavily indebted government would be unable to pay salaries next month.
Tammam Salam also said Lebanon’s inability to service the public debt through bond sales could result in the country’s credit rating falling down to the ranks of the “failed states”.
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