Adam Hamawy, a plastic surgeon and U.S. Army veteran whose parents emigrated from Egypt when he was seven months old, is running for Congress as a healer, of sorts. He has traveled on humanitarian missions in conflict zones, including Gaza. And he has put the issue of health care at the center of his campaign for New Jersey’s 12th Congressional District, saying that money spent on war should instead be used for universal Medicare coverage.

“I go to disaster areas, and that’s where I’m needed now,” Dr. Hamawy said in an interview, referring to Capitol Hill.

He has emerged as a front-runner in the extraordinarily crowded race to fill the seat being vacated by the retiring representative, Bonnie Watson Coleman. At one point, 17 Democrats were in the mix. The field has since dwindled to a mere dozen, including a well-known former leader of the state’s Working Families alliance, a state assemblywoman, two mayors, a patent lawyer, the owner of a chain of fitness studios and a Princeton University neuroscientist with an expertise in gerrymandering. The winner of Tuesday’s election will be heavily favored to win in November.

Dr. Hamawy has led the race for campaign cash and has landed endorsements from such left-wing luminaries as Senator Bernie Sanders of Vermont and Hasan Piker of the internet, who appeared with him on Saturday for a get-out-the-vote rally in Trenton. A newly formed pro-Palestinian political action committee, American Priorities, has spent more than $1.5 million on ads that highlight Dr. Hamawy’s work as a surgeon — a figure that dwarfs the campaign budgets of every other candidate.

His critics have been trying with growing urgency to highlight an earlier part of Dr. Hamawy’s history: a gap year the future surgeon spent between graduating from Rutgers University-New Brunswick in 1991 and entering the university’s medical school the next year.

It was then that Dr. Hamawy began spending time with Sheikh Omar Abdel Rahman, a blind, militant Islamist who lived and preached in New Jersey. Four years later, Mr. Abdel Rahman would be tried and convicted of inspiring violence that contributed to the 1993 World Trade Center bombing. He died in 2017 while serving a life sentence.