Villaraigosa said an unexpected increase in property taxes would enable him to avoid the drastic steps, the Los Angeles Times reports.
"To all of our surprise, we've gotten an increase in revenues of $30 million more from property tax than we expected," Villaraigosa said Thursday. "We might not be out of cash after all."
On Tuesday, he had said the two-day department closings and furloughs might be necessary to keep the city from running out of money.
But City Council members said the furlough idea had little chance because of opposition from the council and labor.
"He can't furlough employees without the concurrence of the council," Councilwoman Jan Perry said.
The council's chief legislative analyst "made clear that that was not an action that could be taken unilaterally," Perry said.
Council President Eric Garcetti said efforts to close a $212 million budget gap shortfall could raise reserves to nearly $40 million by the end of the fiscal year.
"There's no scenario, unless something catastrophic happens, where we are going to be in the red," Garcetti said.
Acting city Administrative Officer Ray Ciranna said a report on the city's financial outlook, to be released Friday, would show "things are not as dire as once anticipated."
"We are still in a budget crisis, but we will end the year paying all of our bills," he said.