A £1m fund has been set aside by a council to replace cladding on two towers after samples failed safety tests.
The checks on the Evenlode and Windrush blocks in Blackbird Leys, Oxford, were ordered after the Grenfell Tower fire.
Oxford council is unhappy the government will not pay and said ministers had pledged to do so.
A government spokesperson said it would ensure restrictions on council funds did not stop works from happening.
The city council said it would be looking at "every opportunity" to make the government contribute.
"We have a million pounds but we'd rather be spending it on something else, and we will be telling the government that loud and clear," councillor John Tanner said.
The final bill for replacing the cladding on the towers could still rise, councillors on the executive board warned.
A review of building regulations is taking place following the Grenfell fire and the board said more work could be needed if rules are changed.
The extra £1m from the council's housing budget will not affect investment in other projects, a council officer report confirmed.
Oxfordshire's fire service has said residents are safe to remain in the towers, which both have sprinkler systems fitted.