Salam said that if a cabinet meeting scheduled for Thursday was not productive on issues including a tender to decide on a new refuse collection company, "there would be no necessity for the government after it".
"I warn that we are going towards collapse if matters continue," Salam said in his address earlier in the day.
"Frankly, I have not and will not be a partner in this collapse. Let all officials and political forces bear their responsibilities."
Should Salam resign, a caretaker government would stay on. His resignation would, however, trigger a constitutional crisis. In Lebanon, it is the president who appoints the prime minister.
But the presidency has been vacant since Michel Suleiman's term expired more than a year ago, and filling it requires a political deal many believe can only be brokered by Iran and Saudi Arabia.
"The trash is the straw that broke the camel's back, but the story is much bigger than this straw," Salam said. "It is the story of the political garbage in the country."
Read MoreLebanon PM threatens to resign as protesters rally in Beirut
He warned the heavily indebted government would be unable to pay salaries next month. Unable to issue new debt, Lebanon risked being classified "among the failing states".
The country's public debt stands at about 143 percent of gross domestic product, a government source said.
Salam vowed to bring to account officials responsible for what he described as an excessive use of force on Saturday.
New York-based Human Rights Watch said police had failed to uphold human rights standards and urged an investigation.
The trash crisis began last month when the main refuse tip for Beirut was closed, with no ready alternative. While collection has resumed, no solution has been found.
Lebanon, still rebuilding from its 1975-1990 civil war, has been jolted by spillover from the Syria war, including political violence and a flood of refugees.
Hezbollah, a powerful Iranian-backed party, is fighting alongside President Bashar al-Assad in the Syrian conflict.