ALBANY, N.Y. — Mayor Bloomberg warns that Gov. Andrew Cuomo’s proposed state budget will cut city funding by more than $2 billion, trigger thousands of layoffs and force cutbacks that include closing a third of senior centers if it isn’t changed by the Legislature.

Cuomo puts the cut at about $1 billion.

Bloomberg told lawmakers at a hearing Monday that they can legislate relief from state mandates that would ease the impact of inevitable cuts.

He called again for legislation to allow principals to lay off as many 6,000 teachers based on merit and performance, rather than strictly by who’s most senior. Otherwise, Bloomberg says, all schools will face a “merry-go-round” of lost teachers and replacements as well as the loss of motivated younger educators.