Amalgamated Workers Union assistant secretary Lindsay Chappell said: "We are currently putting a written request forward for [City Care to give] some consideration to workers. They are the people at the front line."
Some had worked 24-hour stretches after the quakes, he said.
"There's no denial these people put in the effort and probably a darn site more than someone behind an office desk," he said.
The city council yesterday declined to comment on the City Care issue.
Just under 2000 city council staff will be eligible for the days off, which have been called staff support days.
City Care achieved a strong financial performance for the year ended 30 June 2012, returning a net profit after tax of $16.5 million and a substantial increase on the previous year's profit of $11.3 million.
Revenue for the year increased considerably from $237 million in 2011 to $354 million, a rise of 48 per cent. The increase in revenue is largely as a result of the work undertaken after Christchurch's earthquakes and aftershocks.