This is what happens when you look a gift horse in the mouth.

A group of business leaders had tried to work with the Boston Police Foundation, a charity that raises funds to assist the city’s officers, to bring back mounted police patrols. Several pledged to give $100,000 apiece, enough for one horse and related equipment, two years ago.

But the foundation’s board decided against it. So now a few former and current members have formed their own nonprofit, called Friends of the Boston Police. Their first project: bringing back the horses.

“We just had a different vision,’’ said Sean McGrath, president of the Natick real estate development firm Stonegate Group and a cofounder of the new ­charity.

He said his group will shoot for bigger, bolder causes than does the Boston Police Foundation, which concentrates on more modest enterprises, such as getting gym equipment for precinct stations. “They just didn’t have it on their mind to think on a larger level,’’ said McGrath, whose family’s foundation pledged $100,000 for the horses.

The chairman of the Boston Police Foundation, Carl Jenkins, said the horse project didn’t really fit with his group’s primary focus: improving the health and wellness of the officers.

“It’s a PR thing for the city; people love seeing officers on horseback,’’ Jenkins said. “But it’s not just about how much money you need to buy the horses. There are officers that need to be trained, support staff that are needed, vehicles that are needed, veterinarian bills, food. It’s a lot of money.’’

It may seem strange to have a falling out over such a charitable enterprise. But the mounted unit holds a cherished spot in the city’s history, and its revival could offer bragging rights, civic pride, and favorable publicity for the business leaders who pull it off.

Former foundation members McGrath and George Regan, the PR impresario, started the new group. They were joined by consultant Lawrence Curran, who remains on the boards of both organizations. McGrath said about half of 10 or so board members he has lined up so far have some current or former connection to the foundation. Ideally, he envisions the Friends group tackling at least one $1 million-plus project a year.

Boston once had the oldest mounted police force in the country, but it was shut down by then-Mayor Thomas N. Menino in 2009 as part of a wave of budget cuts. In 2016, businessman Herb Chambers was having lunch with Police Commissioner William Evans and asked him what he could do to help the department. Evans suggested reviving the mounted patrols. Chambers was among the first to agree to donate $100,000.

McGrath and Regan began championing the cause and tried to get the police foundation to go along. Mounted police, they argued, are the most effective way to control crowds, such as during the Boston Marathon or celebrations after a major sports victory. Horses, they added, also help officers to connect with residents in the neighborhoods, particularly kids.

But a majority of the police foundation’s board decided against the horses, because they would saddle the department with extra operating expenses and the project isn’t consistent with the foundation’s core mission.

So to continue the cause, McGrath and Regan decided the next best thing was to start their own organization. McGrath said he has at least $700,000 in pledges so far — enough for seven horses.

A spokesman for Evans said the commissioner still wants to bring back mounted police, although it is unclear where the horses would be stabled. There’s no room at the stable in Franklin Park where the city keeps the Parks and Recreation Department’s seven horses.

Mayor Martin J. Walsh had pledged in 2014 to bring back police horses, soon after the start of his first term in office. But it’s unclear if City Hall is still along for the ride. Asked if Walsh still favors bringing back horses, a spokeswoman responded with a brief written statement that made no mention of them, but instead focused on other public safety initiatives.

Meanwhile, the original foundation isn’t missing a beat, Jenkins said. The all-volunteer group raises between $500,000 and more than $1 million annually, depending on the year. A number of prominent business people remain on the board, and the group drew retired Red Sox slugger David Ortiz and Boston Globe managing director Linda Pizzuti Henry to its annual gala last fall.

“We’re proud of our mission,’’ Jenkins said. “I don’t sense at all that anybody is sitting around wishing, ‘Geez, we should do the horses.’ ’’

Jon Chesto can be reached at jon.chesto@globe.com.