BOSTON (AP) — Some Massachusetts voters see Sen. Edward Markey as potentially vulnerable to a primary challenge, and one group is even trying to persuade U.S. Rep. Joe Kennedy to run for his seat.

Markey, a Democrat, has represented Massachusetts in Congress for decades — first in the House before winning John Kerry’s former Senate seat in 2013 — but the state saw an incumbent lose just last year as Democrats elected more women and minorities.

Ayanna Pressley defeated longtime incumbent U.S. Rep. Michael Capuano in the Democratic primary and went on to become Massachusetts’ first black woman elected to the U.S. House.

Markey already has two declared primary challengers, and now a group has launched a bid to draft Kennedy. The congressman has said he doesn’t want the seat.

The group praises Kennedy as progressive and says he could stand up to Majority Leader Mitch McConnell. Members want Kennedy to run not just because of his last name — he comes from a line of senators — but because he supports gay rights as well as action on climate change and gun violence.

“This has nothing to do with Ed Markey,” said Kim Spencer, a 63-year-old Newton resident, who is part of the group. Kennedy “is always on the right side of the issues for us. We thought it was time for him to step forward and take up this challenge.”

Emily Kaufman, a spokeswoman for Kennedy, said he appreciated the effort but isn’t interested.

“On the draft effort, Congressman Kennedy is humbled by the support from folks across Massachusetts,” Kaufman said in a statement. “As he has stated before, he is running for re-election in the 4th District.”

Giselle Barry, a spokeswoman for Markey’s office, said the senator is running for re-election “no matter who enters the race.”

“He is crisscrossing the state and will run his campaign hard every day,” she said in a statement.

Markey is already facing a challenge from Shannon Liss-Riordan, a workers’ rights lawyer who says she’s spent her career representing workers who have been taken advantage of by their employers, including servers whose bosses were taking their tips. She’s a graduate of Harvard Law School and Harvard College.

Steve Pemberton, a former senior executive at Walgreens, has also announced his candidacy, saying he would focus on issues like education, health care and “the collateral impacts of income inequality.” He graduated from Boston College.

As of the end of June, Markey reported having more than $4 million in his campaign account.

Liss-Riordan reported raising more than $1.1 million since she announced her campaign this year. The vast amount of that total — $1 million — came in the form of two $500,000 loans from Liss-Riordan herself to the campaign.

Pemberton’s campaign announcement came after the latest campaign finance filing deadline.

Kennedy reported having more than $4.2 million in his campaign account as of June 30.

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