The expected victory means Labor will notch up 23 years in office by the end of the coming term.
"We've had an extraordinary series of challenges thrown at us, as a city and as a community, and we've got through it because we've worked together," he said.
"We've got through it because we've applied progressive values to our government decisions and because we've applied compassion and we haven't left people behind."
With counting due to continue well into next week, Labor appears to have won at least 11 seats and the Greens three, out of the 25-seat assembly.
The Liberals could hold as few as eight seats, with the Greens securing as many as six if preferences go the minor party's way.
Labor's primary vote was hovering at just over 38 percent, while the Liberals polled 33 percent and the Greens just under 14 per cent.
Liberal campaigners sheeted home the Labor win to the benefits of incumbency as the coronavirus pandemic continued and the difficulty of campaigning amid a global crisis.
Coe did not indicate whether he would stand aside as leader.
The Greens received a swing of just over three per cent swing while the Liberals copped a slightly larger swing against them.
Greens leader Shane Rattenbury, who has been a cabinet minister in the minority government, said Canberrans have voted for action on climate change, inequality and housing affordability.
He said he would have an "interesting conversation" with the chief minister this week, as the Greens sought to "reset" the arrangements with Labor.
No postal votes were counted on Saturday night and the final determination of seats won't happen for at least a few days.
Liberal member Mark Parton said it had been a difficult environment in which to campaign.
"What we are seeing here is the result of an election campaign when you couldn't really have an election campaign," he said.
Retiring veteran Liberal Vicki Dunne said eight seats would be a "terrible" result for her party.
"There will have to be some real soul searching as to whether the campaign was good enough," she said