The Greek government has so far been unable to persuade the striking garbage collectors to return to work after huge piles of trash accumulated on the streets of Athens.
Garbage collectors on strike scuffled with riot police in central Athens outside the entrance of the Interior Ministry building, where a union delegation presented its demands.
Nikos Trikas, leader of the municipal workers' union, said the strike would continue at least until Thursday, with more protests planned on that day.
"The government rejected our demands in three minutes. They have taken their decisions and will allow private contractors to participate in garbage collection," Trikas said, surrounded by dozens of striking workers wearing orange caps to shield themselves from the sun.
He said his union would formally request a meeting with Prime Minister Alexis Tsipras on Thursday.
"Basically, they are selling us out, and 10,000 (municipal) workers have no idea what their future will be."
Government officials accused the union representatives of abruptly ending the talks.
With a heat wave expected later this week and temperatures expected to reach 42 degrees Celsius in Athens, the public health agency issued a warning over the continuing strike.
"The continued accumulation of garbage ... combined with high temperatures poses a risk to public health," the state-run Center for Disease Control and Prevention said.
Despite the strike, municipal crews agreed to collect some garbage in busy tourist areas, outside hospitals and at intersections where tumbling piles of trash were slowing traffic.
Striking unions are demanding that the government fulfil commitments to provide permanent jobs for long-term contract workers – an action that could breach strict budget obligations set out under the Greece's international bailout agreements.
Greece has been repeatedly criticised by the European Union for its heavy reliance on open landfills and low rates of recycling, and has been fined on many occasions for failing to close illegal dump sites.