Extinction Rebellion said it planned to "peacefully disrupt the UK Parliament in London" with 10 days of demonstrations until MPs backed the Climate and Ecological Emergency Bill.
Other planned events in the capital include a "carnival of corruption", which is due to take place outside the Treasury, and a "walk of shame" near the Bank of England.
Protester Karen Wildin, a 56-year-old tutor from Leicester, said: "I'm here today because I have serious concerns about the future of the planet - we need to put this above anything else.
"Never mind Covid, never mind A-levels, this is the biggest crisis facing us and we need to raise the message as loudly as possible.
"Not a lot has been done on this issue, everyone needs to hear the message."
Sarah Lunnon, a member of Extinction Rebellion, said: "The failure to act on this issue will have a catastrophic impact on the future of us and the generations to come.
"We want to occupy Parliament Square to make our voices heard. Of course we're in the middle of a pandemic but we're balancing the risk, this is the biggest issue facing us."
The Metropolitan Police said Tuesday's gathering could only take place off the main roads at Parliament Square Gardens between 08:00 BST and 19:00. Boats, vehicles, trailers or other structures were banned from the procession.
The same rules apply for Wednesday's demonstrations.
The Met said as of 18:00 Tuesday a total of 90 people had been arrested on suspicion of public order offences.
Footage posted online by Extinction Rebellion appeared to show John Lynes, a demonstrator in his 90s, being led away by police near Parliament Square while walking with a stick.
Mr Lynes, from St Leonards-on-Sea in East Sussex, has joined previous protests organised by the group.