By Alina Selyukh

WASHINGTON (Reuters) - U.S. Republican presidential contender Rand Paul said on Sunday he plans to push Congress to cut federal funding for the non-profit reproductive healthcare organization Planned Parenthood in a debate over its treatment of aborted fetal tissue.

"I think the time is now to discuss whether taxpayer dollars should be going to such a gruesome procedure," Paul, a Kentucky senator, said on Fox News Sunday. "People are outraged by this and I think the American people deserve to have a vote on it."

Senate Majority Leader Mitch McConnell has started a fast-track process to bring Paul's legislation for a vote soon, McConnell's spokesman told Reuters on Sunday.

Republicans have rallied around secretly recorded videos showing Planned Parenthood officials discussing ways to perform abortions to preserve fetal tissue for research, as well as the costs involved. The videos were filmed by anti-abortion group Center for Medical Progress.

Paul has urged cutting the nearly $500 million in annual taxpayer funding for Planned Parenthood in the latest Republican effort to limit government support of the group over its abortion services.

A woman's right to abort a pregnancy has for decades been a highly politicized and hotly debated topic throughout the United States. Republicans now control Congress and, with it, government purse strings.

Republican lawmakers have called on the U.S. Justice Department to investigate whether Planned Parenthood illegally profited from selling fetal tissue, as well as to report how the department enforces abortion regulations and the ban on late-stage abortions. Democrats have called for a federal investigation of how the group obtained the videos.

Planned Parenthood has flatly denied all allegations. Its president, Cecile Richards, on Sunday said that the group "does not at all" profit from fetal tissue donations and that alteration of abortion procedures to better collect tissue is "absolutely not done."

"Planned Parenthood has broken no laws," she said on ABC's "This Week," adding that donation of aborted fetal tissue for scientific research is only allowed in a few states, with strict guidelines.

"We should not base any kind of decisions about healthcare in this country based on highly sensationalized folks who are nothing but militant anti-abortion extremists," she said.

U.S. Attorney General Loretta Lynch has said the Justice Department would review "all the information and determine what steps, if any, to take at the appropriate time." Two committees in Congress have launched probes.

Interviewed on the CBS program "Face the Nation," Paul said: "My legislation won't be about whether it's legal or not ... I think everybody in America is horrified by this, and they don't want their tax dollars going to this group."

REPRIMANDS FOR WORKERS

Richards said the workers who appear in the videos have been reprimanded for their tone. She has previously apologized for the tone and statements of the filmed comments.

Planned Parenthood says in some cases when aborted tissue is donated, the organization receives reimbursements for the costs of delivering it to research centers, calling that a standard medical practice.

Democrats, including presidential contender Hillary Clinton, have defended Planned Parenthood, which provides various low-cost and free health services to women.

Abortions comprise 3 percent of Planned Parenthood's health services, according to the organization's website. About 40 percent of the non-profit's funding comes from government sources, including Medicaid managed-care plans.

Paul and rival Carly Fiorina raised ethical questions about the collection of aborted fetal tissue on Sunday talk shows. The two are seeking the Republican nomination in the campaign for the November 2016 election.

Before the videos were released, Republicans in the House of Representatives had moved to eliminate about $3 million in federal funding for a family-planning program involving Planned Parenthood. The budget cut was approved by a House committee late last month and is awaiting a House vote.

Paul said he was pursuing several strategies, including a so-called discharge petition requiring the support of at least 16 additional senators to force a vote on Planned Parenthood funding.

He earlier sought to attach a defunding amendment to transportation legislation. But on Sunday he said, "they may block me today on a vote on an amendment to the highway bill," and if so, he would pursue separate legislation.

(Reporting by Alina Selyukh; Editing by Lisa Lambert and Howard Goller)