More than 200 people have signed a petition asking the prime minister to overturn the Grade II listing of council offices in Devon.
The council estimates it could cost £40m to refurbish the skyscraper
The listing of Plymouth City Council's Civic Centre means the crumbling 14-storey building is protected from planned demolition.
The council "vigorously" opposes the listing of the city centre skyscraper and says it could result in job losses.
The listing was proposed by the Twentieth Century Society (TCS).
It said Plymouth should be proud of the Civic Centre.
A Grade II listing recognises a site's special interest and warrants every effort to preserve it.
Barry Keel, the council's chief executive, said the protected status could "impact on services - and potentially on jobs".
He described the private meeting on Tuesday as "useful".
"We were able to outline our position and why we - and so many people in Plymouth - are so vigorously against this listing," he said in a statement.
"We outlined why we do not agree the building is architecturally important; and what listing will mean to the city's economy, our services, the community and the regeneration of the city centre."
Mr Keel added the council was continuing to look at all its options for overturning the listed status.
The decision by the Department for Culture Media and Sport to award Grade II listing to the Plymouth city centre skyscraper has been criticised by the city's three MPs: Gary Streeter, Alison Seabeck and Linda Gilroy.
They joined forces in a cross-party bid to ask English Heritage to reconsider its decision.
An English Heritage spokesman described the building, which was opened by the Queen in 1962, as an "an iconic feature in the centre of Plymouth".
But Plymouth Civic Society has disagreed with the description.
Spokesman Peter Towey said: "It was cheap and nasty and it remains cheap and nasty."
The council estimates the bill for refurbishing the crumbling building could be about £40m now it is listed.