John Fetterman has placed abortion rights at the top of his agenda to capture Pennsylvania’s Senate seat in November, telling supporters at a raucous rally on Sunday: “Women are the reason we can win. Don’t piss off women.”

The Democrat was targeting comments made by his Republican opponent Mehmet Oz in May that abortion at any stage of pregnancy was “murder”.

Oz, in keeping with a recent trend among Republican candidates, has attempted to soften his extremist position as the fall’s midterm elections draw closer, insisting that he now believes in exceptions for rape, incest and the health of the woman.

But Oz’s rival was uncompromising in his criticism during Sunday’s rally at a community college in rural Pennsylvania attended by several thousand supporters, including a large number of women in pink “Fetterwoman” T-shirts.

“This decision is between a woman and a real doctor,” Fetterman said of abortion, alluding to Oz’s status as a celebrity television doctor who has been branded by medical ethicists as a “huge danger to public health”.

“Oz believes abortion is murder,” Fetterman continued. “If every abortion is murder, that means Oz thinks every woman who had to choose an abortion is a killer. Think about that.

“Women are the reason we can win. Let me say that again. Women are the reason we win. Don’t piss women off.”

According to research by TargetSmart, a polling analysis company, Pennsylvania ranks fifth in states showing large gaps in registration numbers between men and women since the US supreme court in June overturned the 1973 Roe v Wade decision that established federal abortion rights.

Pennsylvania joins Arkansas with 12% more women than men registering, while Kansas – a staunchly Republican state where pro-choice advocates won a massive victory last month retaining constitutional protection for the procedure – leads the country with a 40% gap.

Democrats are attempting to channel nationwide anger at the reversal of Roe, and the escalation in anti-abortion legislation by Republicans in several states, into success in November’s elections.

The Democratic party faces an uphill battle to retain control of both congressional chambers, but it is encouraged by research showing that voters are outraged at the ending of nearly half a century of federal abortion protections.

A Pew Research poll last month showed abortion was an important factor for 56% of registered voters, up from 43% in March. Among Democratic voters the figure rises to 71%.

In Pennsylvania, the candidates are locked in a tight race.

Fetterman has painted Oz as a “visitor” from New Jersey who knows little about the state he wishes to represent. Oz’s campaign, meanwhile, has mocked the health of Fetterman, who is recovering from a stroke.

According to the Philadelphia Inquirer, Fetterman – who has said he is struggling with auditory processing issues since his stroke – spoke for about 10 minutes Sunday, and he did not appear to stumble over as many words as in other recent appearances.