Boston Mayor Thomas M. Menino began his new term Monday by reaching out to Harvard, openly inviting expansion of Harvard medical facilities into the Crosstown area of Roxbury.

“If Boston has a friend in President Larry Summers, then Harvard has a friend in City Hall,” Menino said in the first speech of his third term before an audience that filled Faneuil Hall.

A main focus of Menino’s speech was seeking partnerships and funding from non-profit and educational institutions as a way to fund new programs in the face of tighter city budgets.

“I see a new era of partnerships with our colleges, universities and non-profits,” Menino said. “We need them to be more involved with the city.”

That approach could have a great impact on relations with Harvard, itself an $18.3 billion non-profit educational institution.

However, Harvard officials said they view Menino’s comments not as a change so much as a continuation and expansion of previous cooperative town-gown relations.

“We’re open to any opportunity to cooperate with the city,” said Kevin A. McCluskey, Harvard’s director of community relations, who specializes in relations with Boston. “The mayor has always been a strong advocate of partnerships and this is consistent with his past approaches.”

Menino lauded the joint effort between the city and local colleges and universities to increase student dorm spaces in order to ease Boston’s housing crunch, and cited it as a model example of successful partnerships between government and higher educational institutions.

Tax-exempt non-profit institutions, such as universities and hospitals, own 51 percent of Boston real estate, significantly shrinking the city’s tax base. Harvard now owns more property in Boston than it does in Cambridge, even without including Harvard’s many affiliated hospitals and research institutions.

Although it does not pay taxes, Harvard and some other non-profits make payments in lieu of taxes.

Menino noted that these agreements will be up for renewal in his coming term, and vowed to make educational institutions accountable.

“We can’t just renew these agreements without applying today’s standards,” Menino said. “What I’m asking for is accountability.”

Menino proposed using funds paid in lieu of taxes to create scholarships or job training programs.

In a proposal he first put forward last month, Menino also called for the development of a “thriving medical area at Crosstown,” an area of Roxbury that abuts Harvard-affiliated hospitals and research facilities. For the first time, he specifically called on Harvard and Summers to take an active role in the realization of that goal. The mayor said that such a complex would strengthen the neighborhood and create jobs.

“I want to strengthen our partnership with Harvard. I want to invite President Larry Summers to explore what Harvard could do to expand its medical school complex to Crosstown in Roxbury,” Menino said.