Quincy officials and a bar owner say they are working together to legalize a mural that blends the image of Barack Obama with Jimi Hendrix and that has received an outpouring of support from residents.

According to David Keville, co-owner of Presidents Rock Club, the mural, tucked in an alley behind Hancock Street, has been on the side of his business since Labor Day weekend, but no one made a fuss about it until this week.

“The wall had three different surfaces — stucco, brick, and something in between,” Keville said. “It wasn’t very pretty at all. And the kid who told me he was going to do it says, ‘I’m going to put a mural up there,’ and I said, ‘I don’t own the building.’”

The artist, who calls himself Brandalizm, painted the mural anyway.

“I painted Obama to show a sign of the times,’’ the artist said in an e-mail from California. “I could have done Lincoln as Slash, and no comments would have been made. That alley was disgusting and the city never cleaned it.’’

Keville said he and his business partner were out of town when the mural went up, and they discovered it after returning to work.

In addition to depicting President Obama as the iconic rock guitarist, the mural features the Obama campaign symbol with the slogan “Forward” and urges people to “Rock the Vote.”

City officials said the Building Department first heard about the mural this week, when someone called about it.

Mayoral spokesman Christopher Walker, said the Building Department told the bar to paint over the mural because it violated the city’s ordinances, which require murals to receive permission from the Planning Board and the Historic District Commission.

The owner was told that ­until the issue was resolved, he would be fined $300 a day.

New coverage of the city’s action triggered an outpouring of support for the mural. One website started a petition to keep it intact.

When the office of Mayor Thomas Koch learned about the controversy, it decided to take a different approach.

“The Building Department was doing their job and following the code of the city,” Walker said. “In this case, the mayor thought [the artwork] isn’t some grand controversy. If it’s the bar’s desire to get the ­appropriate permit, there is no need to take it down.”

Once the bar obtains the permits, any fees incurred would be waived, he said.

“As far as we’re concerned, it’s artwork, it’s a mural, guided by the zoning code,” Walker said. “And whatever it is, it’s fine if it stays, as long as it goes through the permitting process.”

Observers on both sides of the political spectrum agreed that keeping the mural is the right thing to do.

“I don’t want it to come down,” said Hingham resident Steve O’Connell, who works on Hancock Street and is a Republican.

“It’s a free expression of thought. I just think it’s funny to equate Hendrix with Obama . . . but it doesn’t offend me.”

“There seem to be a lot more things to worry about than a mural,” said Tom Taber, a Quincy resident who said he registered as a Democrat Friday morning. “I would like to see it stay up. Maybe I’ll spend some money to help them pay the fine.”

Keville said he is coming up with a plan to get the mural permitted and that more likely than not, it will remain.

In the meantime, business has increased because of the publicity, and Keville has contacted the Obama campaign to see if the president might come see the work for himself.

Keville said he appreciates all the press, even if it did create some controversy.

“It is a pretty nice thing,” he said. “It evoked a lot of good will.”