Eric Buehrens, the interim president and chief executive officer at Beth Israel Deaconess Medical Center, said the hospital is also committed to the new Payments In Lieu of Taxes (PILOT) plan, even though it calls for Beth Israel Deaconess to increase its contribution from $167,000 this year to $750,000 next year and to $3.1 million after five years.

“My primary goal in life is to make Boston University a better institution, but it can only be a better institution if the city thrives,’’ said Boston University president Robert A. Brown .

Some nonprofit leaders voiced unequivocal support for the initiative during interviews with the Globe, asserting that their success depends in large measure on attracting visitors — students, hospital patients, and culture lovers — to a safe, well-managed city.

But support for the plan — the product of a mayoral task force that included representatives from nonprofits — appears mixed among the organizations being asked to pay.

That is still significantly less than the $404 million nonprofits would pay if they were not tax-exempt. New assessments of the property owned by the city’s 40 largest major nonprofits show that its collective value is $13.6 billion, or the equivalent of more than half of the city’s commercial tax base, which is about $25 billion, according to Boston’s Assessing Department.

The new revenue-raising plan — the first of its kind in the nation — is based on the estimated cost of providing basic city services, such as police and fire protection, snow removal, and emergency medical treatment, which account for roughly 25 percent of the city’s budget. And it is designed to gradually increase annual financial payments to the city by the major tax-exempt organizations from the $15 million they paid this year to $48 million over a five-year ramp-up period.

“We’re looking for fairness for Boston taxpayers and the nonprofits,’’ said Boston Mayor Thomas M. Menino. “This isn’t something we drew up on the back of an envelope. It’s something we put a lot of thought into.’’

Although many of the city’s nonprofit organizations have been making so-called Payments In Lieu of Taxes for decades, this marks a major change to a system that feels to some organizations uncomfortably close to tax bills. Boston officials recently mailed letters to leaders at 40 major nonprofits asking them to pay up to 25 percent of what they would owe if their property were not tax-exempt.

For the first time, Boston’s major tax-exempt institutions — its premier hospitals, universities, and cultural centers — are being asked to make regular voluntary payments to the city based on the value of their property to help offset the rising cost of city services and cuts in state financial aid.

“If you’re asking me if I’m excited about paying taxes, the answer is no,’’ Buehrens said. “But I think we recognize that municipal budgets, including the city of Boston’s, are under an enormous amount of strain, and we think we have to be good citizens.’’

Other nonprofit leaders, however, expressed reservations — or declined comment — not only because of the increased cash contributions suggested by the city, but also because of concern that participating in a plan that calls for making payments based on a percentage of property values might set a precedent that could eventually compromise the tax-exempt status of their institutions.

“We have some boards of trustees that are asking, ‘What are the implications? Does this exist elsewhere in the country? Are there precedents we need to be considering? Are we heading down a slippery slope?’ ’’ said Richard J. Doherty, president of the Association of Independent Colleges and Universities in Massachusetts.

Until now, negotiations about payments in lieu of taxes have been triggered when a major tax-exempt organization proposes new construction or offers to buy property in a transaction that could remove real estate from the city’s tax rolls. Under the new plan, the city is instead asking tax-exempt groups to make regular payments based on property values, similar to ordinary taxpayers.

Still other nonprofit leaders said they are adopting a wait-and-see attitude toward the new plan, pointing to the wide disparity in voluntary contributions to the city that are now made by its largest tax-exempt organizations.

Officials at Partners HealthCare, for instance, owners of Massachusetts General, Brigham and Women’s, and Faulkner hospitals, said they are reluctant to increase their payments beyond the $4.3 million in lieu of taxes paid this year, noting that they already pay much more than other hospitals. Boston Medical Center and Children’s Hospital, for instance, each paid less than $140,000.

“Before we consider increasing the size of our contribution, our view is that other tax-exempt health care providers and other nonprofit institutions that do not make significant contributions should adjust their payments,’’ said Rich Copp, vice president for communications at Partners.

Meanwhile, Steward Health Care System, a for-profit company that recently purchased St. Elizabeth’s Medical Center and Carney Hospital, is expected to pay about $10 million in yearly property taxes, according to Boston assessors, without cutting charitable services to the poor and uninsured.

Over the last few decades, PILOT agreements negotiated individually under the city’s old system have varied widely. This year, for example, Boston University made $5.1 million in voluntary payments — more than any other nonprofit — while Boston College paid just $298,000 and Northeastern University paid about $31,000.