Former New York City Mayor Michael Bloomberg at the National September 11 Memorial Museum. Keith Bedford for The Wall Street Journal

The National September 11 Memorial Museum, which opened to the public this week, is one of many cultural projects championed by New York's former mayor, Michael Bloomberg.

During his 12 years in office, the Bloomberg administration shepherded the construction of the museum. It also served as an incubator for the Culture Shed, a planned exhibition space in the Hudson Yards development on the West Side of Manhattan, and a performing-arts center at the World Trade Center site—a project that faces significant fundraising and logistical challenges.

The 9/11 foundation faces funding hurdles as well. It has raised more than $470 million but is now pushing for $20 million in annual federal funding to support its $63 million operating budget.

Mr. Bloomberg remains chairman of the foundation and last year became chairman of the Serpentine Gallery, a contemporary-art museum in London. He spoke with the Journal about funding for the 9/11 museum and why he won't sit on a board if he's not in charge. Below are edited excerpts from the interview.

Was the 9/11 museum the biggest fundraising challenge you've ever had?

I don't know. I remember the city had to raise $75 million for the Republican convention. The way these conventions work is the cities pay for them, and you have to raise the money privately. That was harder in a city that's all Democrats.

What's your strategy for convincing Congress that taxpayer money should help fund the museum and memorial?

At the moment, Congress isn't funding anything. There's paralysis. So I think at the moment it's not likely that we're going to be successful, but you still have to try. The work you do sets the stage for down the road, when Congress is in a more free-spending mood or the stars are better aligned.

Have you talked with Mayor Bill de Blasio about getting city funding?

No. Because first thing he'd say: Why didn't you put more city funding in when you were mayor?

So I'll leave him alone.

One of the missions of the 9/11 foundation was to help get the performing-arts center off the ground. And it acted as an incubator. That hasn't yet been realized.

I think downtown could use another venue for the arts. It's tougher at the moment. The big push is to get the money for the Culture Shed over on the West Side, which the city desperately needs.

It doesn't seem that we ever have enough performance space. No matter what you do, they all seem to be full and doing well. So I think [the performing-arts center is] a great idea. You can rest assured, I will be a big donor.

Are you concerned it might not get off the ground?

I worry about everything. It is tangential to the mission of the memorial and the museum. It's a great place for it, and it's needed, but I don't know that it has any direct connection.

The Serpentine Gallery—that's a real contrast to being chairman of the 9/11 foundation. What drew you to that?

I can focus on the development side. You do not want me focusing on the curatorial side. [Laughs]

My mother always thought I was a philistine. I used to be on the board and then dropped off when I became mayor. It was a conflict with museums here.

I've said I'm not going to go on any boards ever again, other than if I'm chairman. I'm an executive. I do things. I've had my period of sitting in a board meeting. It's not going to happen again.

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