EU leaders are offering developing countries a three-year deal that would pay them 7.2bn euros (£6.5bn; $10.6bn) to help cope with climate change.
The exact target for limiting temperature rise is unclear amid disputes between various blocs.
Danish police estimate that some 30,000 people joined the march while organisers put the number at 100,000.
They marched 6km (four miles) across the city to the conference centre where negotiators and ministers are meeting.
After violence erupted, large numbers of mainly young people were detained.
TV pictures showed the police putting the demonstrators in seated lines on the street with their hands tied behind their backs. They were later removed on buses.
Henrek Suhr, of Copenhagen police, told the BBC that their intelligence had suggested a small group of people had planned violence.
"We thought... these people would make a lot of trouble in Copenhagen had we not arrested them, and we arrested them because they had done a lot of things before our arrests. They smashed some windows at the foreign ministry," he said.
He rejected claims by climate protesters that some of those being held had been mistreated and denied access to basic needs.
Simon Sheikh, of the Australian social and political network "Get Up", said he had witnessed the detentions from his apartment in the centre of the city.
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