When Mayor Martin J. Walsh takes the stage at the Cutler Majestic Theatre for his second inauguration Monday morning, he will introduce an effort to build 200 units of long-term housing for chronically homeless Bostonians, his office said Sunday.

Walsh will ask Bostonians and local organizations to contribute to the new Boston’s Way Home Fund — established with a goal of raising $10 million over his next four-year term — to construct the residences, according to a statement.

“We are committed to making sure that every person in our city has a place to call their home and build a better life, and this new fund will help do just that,’’ Walsh said in the statement.

“People often ask what they can do to help — I encourage everyone to learn more about Boston’s Way Home Fund, and invite every organization and individual to join us as we move closer to our goal of ending chronic homelessness in the City of Boston.’’

The housing is planned to include rent subsidies as well as support services to help people who face complex issues remain in homes, the city said.

Walsh announced in his 2016 State of the City speech that Boston had accomplished his goal of ending chronic homelessness for veterans. Almost 850 homeless veterans have been housed since he took office in January 2014, according to his administration.

The mayor launched the new fund-raising effort through a partnership with the Pine Street Inn and Bank of America, which contributed seed money of $250,000 to the fund.

Lyndia Downie, CEO of Pine Street Inn, said the shelter is “thrilled to be part of this initiative’’ as it looks ahead to its 50th anniversary in 2019.

Jeremy C. Fox can be reached at jeremy.fox@globe.com.