The Mamdani administration is giving property owners an extra month to apply for an exemption on the state’s controversial new pied-à-terre tax — following massive backlash over its rollout.

New Yorkers with second, one-to-three-family homes valued over $5 million and co-ops and condominiums valued at $1 million will have until Sept. 18 to file appeals, Mayor Zohran Mamdani announced Saturday.

The previous deadline was Aug. 21 for homes and Aug. 24 for co-ops and condos.

The socialist mayor — who lobbied for the new tax — had claimed for months it would only hit wealthy out-of-towners.

But many full-time residents cried foul after Department of Finance mailed them a notice saying that they “may” be on the hook for a five-figure tax bill.

The city in the last week has sent out 17,000 letters alerting property owners they could be subject to the tax — more than the 10,000-13,000 non-primary residences that government officials earlier estimated would be slapped with the surcharge.

“This is really the least this administration can do to begin to fix this train wreck,” said Council Minority Leader David Carr (R-Staten Island).

“Every homeowner should have ample time to appeal this tax assessment, after they have been properly notified. Giving them less than a month in the middle of the summer is a bad joke.”

The new tax, approved by the Democratic-controlled state Legislature and Gov. Kathy Hochul this spring, is expected to raise $500 million for the city budget.