Support for federal funding of Planned Parenthood itself to provide those services was even stronger, according to the Reuters/Ipsos released on Wednesday.
The non-profit's image has taken a hit, the poll found, after an anti-abortion group earlier this year began releasing videos purporting to show Planned Parenthood officials negotiating prices for aborted fetal tissue.
Still, the strong support for federal funds to help Planned Parenthood provide pregnancy tests and other services indicates Republican presidential candidates should tread carefully.
"We have so many young people having babies when they're babies themselves," said Renee Harrison, 57, a Republican from Waldo, Wisconsin, adding that she favored anything that could counter that trend.
Planned Parenthood, which provides health services to millions of women at hundreds of centers nationwide, came under a storm of criticism after the videos were released by an activist group called the Center for Medical Progress.
Planned Parenthood has denied wrongdoing. It says abortions make up just 3 percent of its work.
"Americans know that Planned Parenthood provides high-quality health care in communities across the country, and that's why they overwhelmingly oppose these political attacks," Eric Ferrero, a spokesman for the non-profit, said in a statement.
David Daleiden of the Center for Medical Progress said the videos changed Americans' perception of the health organization.
"The poll shows the more the American people learn about Planned Parenthood's barbaric late-term abortion body parts business, the less they want to subsidize it with their taxpayer dollars," Daleiden said in a statement.
After the videos were released, Republicans in Congress introduced legislation to cut off the more than $500 million in federal funds Planned Parenthood receives each year. That money cannot be used for abortions.
Democrats sided with the non-profit and the measure failed. But some candidates seeking the Republican presidential nomination in 2016 supported the effort.
The Reuters/Ipsos poll shows they should be cautious on women's health issues.
Seventy-three percent of respondents said they supported federal funding for an unnamed group to provide women's health exams, 69 percent backed federal dollars for prenatal services, and 59 percent were in favor of it for contraception. Both Democrats and Republicans polled supported federal funding for the services.
When the question was asked a different way, more participants said they backed federal dollars for Planned Parenthood specifically to provide those services.
Overall, 54 percent supported federal funding of Planned Parenthood, and 26 percent opposed it.
But 44 percent of respondents who saw the videos said they now have a more negative view of Planned Parenthood, compared with 34 percent who said their views were unchanged.
"I just don't think they ought to receive my money that I pay in taxes," said Kathy Scholl, 66, a Republican from Iowa Park, Texas.
After the videos were described to poll respondents, 39 percent said Planned Parenthood should not receive government funding and 34 percent said federal dollars should continue.
The online poll had a credibility interval, a measure of accuracy, of 3.1 percentage points.