Over the last five weeks, five candidates pulled papers to run for Boston City Council seats in this year’s election. While there’s nothing unusual about the timing — savvy candidates know an early start can be key to successful fundraising — three of the candidates share an employer who some say has played an outsized role in Council politics.

At-large candidates Alexandra Valdez and Samuel Onuoha and District 7 candidate Samuel Hurtado all work for Mayor Michelle Wu. Should any of them win the election in November, they could significantly expand the mayor’s influence over the 13-member Council.

That prospect has some political observers expressing concern.

“For anybody who’s running for office coming out of City Hall, it’s incumbent on them to make clear that they’re an independent person, even if they’re aligned on the mayor on a number of issues,” said Jonathan Cohn, policy director for Progressive Massachusetts. “The Council should exist as its own form of government.”

Currently on the body are three councilors who were elected after serving in the Wu administration: Sharon Durkan, Enrique Pepén and Henry Santana.

Mayoral influence on the Council reared its head last June, as the body debated amendments to the mayor’s budget, seeking modest cuts to the Boston Police Department budget and investments in other areas. After Wu vetoed the council’s changes, Pepén and Santana joined the body’s three conservative-leaning members in blocking an override while Durkan sat out the council hearing.

It was a minuscule piece of the city’s $4.6 billion budget — threetenths of a percent. But it was a demonstration of the mayor’s power — power some fear could grow if more members of her administration are elected to the Council.

“Boston city councilors don’t work for the mayor,” said Fatima Ali Salaam, who heads the Greater Mattapan Neighborhood Council.

“They work for their constituents. They’re not appointees. You worry when someone gets into office and feels they’re beholden to a person in higher office.”

Valdez did not respond to requests for comment. Onuoha, who began working in city government under the mayoral administration of the late Thomas Menino, said he is not running with the mayor’s backing.

“I let the mayor know I was running out of respect,” he said. “The mayor was noncommittal to me. She’s focused on her own campaign, as far as I can tell.”

Hurtado, who is running for the District 7 seat currently held by Tania Fernades Anderson, said he’s running without the mayor’s blessing.

“I think this district should stay independent,” he said. “If I win, I’m going to be accountable to the residents of District 7.”

Wu will face off against philanthropist Josh Kraft in her bid for reelection this year. But it’s not uncommon for mayors to direct their political machines — often staffed by city workers — to support their favored Council candidates.

Former District 4 Councilor Charles Yancey, who was in office during the administrations of former mayors Kevin White, Thomas Menino and Martin Walsh, said the Council should serve as an important check on mayoral power.

“It’s important for elected officials to take their duties seriously,” he said. “Their votes on the council should be rooted in the people who elected them, not the chief executive.”

While Wu served on the council with many of the current council members and was considered a member of the body’s progressive majority, she has broken with many of the progressive policies she championed while on the body, including a push to cut spending on the police department and redirect funding to programs and city departments that prevent crime. In last year’s budget negotiations, Council President Ruthzee Louijeune and the body’s progressive-leaning majority called for a $3 million cut to the department’s $454.9 million budget, with funding redirected to the Boston Centers for Youth and Families, fire and transportation departments.

The Council sought to use a power the body won through a 2021 citywide ballot question that Wu supported while serving as a councilor, giving them the power to amend line items in the city’s budget, a power the body did not previously have.

“The housing justice movement, the economic justice movement, unions worked to give the Council more power than they had before,” said Jonathan Rodrigues, a member of the group Mijente. “We need the Council to protect the city’s most vulnerable residents.”

But after Wu vetoed the body’s amendments to the budget, the body needed a two-thirds majority to override the veto. Because the conservative-leaning councilors — Ed Flynn, Erin Murphy and John FitzGerald generally oppose cuts to police funding, Wu needed Pepén and Santana’s votes to block the override.

In the end, with Pepén and Santana’s opposition, the mayor’s vetoes of the Council’s amendments stood.

Some progressive activists worry that scenario will replay itself in the coming years if more councilors feel beholden to the mayor. As Wu’s stance on issues ranging from policing to education becomes less progressive than those she took on the Council, an expanded bloc of her supporters could undermine the checks and balances the body can put on her administration.

“You want the Council to constructively engage the policies the mayor puts forward,” said Progressive Massachusetts’ Jonathan Cohn. “The council should exist as its own form of government.”