The Massachusetts Senate unveiled its version of a major housing bill Monday, following up on similar proposals by Gov. Maura Healey and the Massachusetts House.

Lawmakers hope to approve a compromise version of the bill and get it to Healey’s desk before the end of the Legislature’s formal session on July 31 as the state continues to struggle with soaring housing costs.

The bill’s unveiling comes as Gov. Maura Healey and Boston Mayor Michelle Wu announced Monday that the state will offer $15 million in funding to help Boston convert larger-scale office buildings to housing.

Wu has pushed for the conversions to add more housing after some office buildings failed to fill up again with clients after they emptied out during the pandemic. The conversion can often be costly due to the complexity of the projects.

The state funding would fund up to $215,000 per affordable unit with a cap of $4 million per project. The City’s program application deadline will be extended to Dec. 31.

The Senate’s $5.2 billion housing bond bill failed to include a plan backed by both Healey and Wu that would let cities and towns impose a fee on the sale of high-end properties. The House version of the bill also excludes the proposal, which was championed by housing advocates.

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Greg Vasil, CEO of the Greater Boston Real Estate Board, praised Senate leaders for rejecting the proposal. He said lawmakers need to prioritize policies that “reduce barriers to housing creation, which will in turn help generate production of homes across all price points.”

Among the proposals in the Senate bill is $800 million for the Affordable Housing Trust Fund to create and preserve affordable housing for households whose incomes are not more than 110 percent of area median income.

The bill would also allow $425 million in bonds to support housing preservation, new construction and rehabilitation.

Democratic Senate President Karen Spilka said the Senate bill is designed to help spur production and preserve and promote access to housing.

The bill would also establish the Fair Housing Office with the goal of eliminating housing discrimination and combat the fallout of decades of racially biased housing policies, she said.

“The bill upholds the Senate’s commitment to regional equity by designating discrete authorizations for programs for rural and small towns, midsize communities, seasonal communities, and more,” Spilka and other top Senate Democrats said in a joint statement.

The House bill includes $6.5 billion in bond authorizations, tax credits, and policy initiatives designed to increase housing production, streamline affordable housing development, and preserve existing public housing in Massachusetts.

The Senate is set to debate the bill on Thursday.