Mayor Marty Walsh said during a radio appearance on Friday there are ongoing discussions about including pro-LGBT groups in the St. Patrick’s Day Parade in South Boston. In an interview on WGBH’s “Boston Public Radio,” Walsh said he was hopeful that a compromise can be worked out, since there are fifty-plus days before the parade starts in March.

“I would love to march in the St. Patrick’s Day parade this year and we have to make sure it’s inclusive,” he said. “And I’m going to be working with some folks to hopefully see what we can do.”

“So you think there’s some room for some compromise here?” Boston Public Radio co-host Jim Braude said.

“Absolutely,” Walsh said.

Separately, Walsh said he is aiming to have a new school superintendent in time for the new school year this fall, but he isn’t in a rush, either. John McDonough is doing a “great job,” he said. At some point in the next week a search committee for selecting a school superintendent, Walsh said.

The full interview is available here. The interview was part of an "Ask Marty" segment that the mayor is participating in on the last Friday of every month.

Walsh also discussed the death penalty, bulldozing Government Center and former Mayor Thomas Menino:

-- Reiterating what he told reporters inside City Hall on Thursday, Walsh said he supports U.S. Attorney General Eric Holder’s decision to pursue the death penalty in the case against the Boston Marathon bomber.

Walsh, who voted against the death penalty as a state representative, says he has not changed his personal opinion on the policy. “I personally feel life in prison without parole for the rest of their life is a far greater penalty than putting them out of their misery with the death penalty,” he said. “And you know it’s a tough issue particularly here with Marathon Monday and the bombing and [it’s] so close to home, so sensitive here in Boston.”

-- Walsh said he saw former Mayor Menino at a recent awards dinner. “He looks great. Angela's car got stolen...I can't believe it.” Walsh said the car, which was a rental, was later recovered. He said he has asked Menino for advice on several issues. “He told me his phone is always on for me.”

-- Margery Eagan, Boston Public Radio co-host, pointed to his campaign pledge to tear down City Hall. “That’s probably not going to happen,” she said.

“Well, hold on,” Walsh cut in. “You know, I’m 26 days in…It’s not the top of the list but it’s something we have to look at.”

He added: “I’m sitting in the mayor’s office, I look up and the ceilings are about 75 feet up in the air and I’m thinking we can put about three more floors of people in here. Maybe I’ll build a loft.”

“But you’re serious about this,” co-host Jim Braude said.

“I’m serious about doing something,” Walsh said.

-- Expressing support for PILOTs, or payments in lieu of property and other taxes, from colleges and nonprofits, Walsh said he wants to review some of the agreements. Some organizations are “great,” he said, while others refuse to pay City Hall.

-- Walsh said he was looking for input on what can be improved in the city of Boston. “Criticism is good. Criticism makes you stronger.”