Mayor Michelle Wu has vetoed millions of dollars in cuts the City Council tried to push through for the Boston Police and Veterans Services departments following days of backlash.

Wu also rejected the entirety of cuts proposed for the Public Works and Transportation departments, totaling more than $5 million, along with the Boston Public Library, Boston Centers for Youth and Families, and the Equity and Inclusion Cabinet.

In a Friday letter to the City Council, Wu called the Council’s attempt to slash nearly $31 million from the Boston Police budget “illusory, as the city is obligated to cover salary and overtime expenses incurred by the department”

She also said plans to cut from departments like the Office of Veterans Services, where the Council had approved a $900,000 reduction, “would reduce critical programming and limit our ability to fund future obligations.”

“Our returned budget also includes rejections, because the scale and scope of amendments passed by the Council would result in reductions to core city services that our residents depend on and deserve,” Wu wrote.

“Our budget must be responsive to the needs of our constituents, fiscally responsible, and built on a foundation of effective delivery of city services that are central to our residents’ quality of life.”

The $4.2 billion operating budget approved by the City Council via a 7-5 vote Wednesday included roughly $52.9 million in amendments to Wu’s initial proposal.

Substantial cuts to the Boston Police and Veterans Services departments sparked an immediate outcry. The cuts would have slashed $22 million from police overtime and reduced the veterans budget by roughly 14%.