Protests against Planned Parenthood, a non-profit organisation that provides reproductive services, took place across the US, the media reported.
#ProtestPP, a national coalition opposed to abortion rights that seeks to end any public funding for Planned Parenthood, said more than 200 rallies were planned in 45 states on Saturday.
"The time has come to defund America's abortion giant," #ProtestPP said on its website. "Join us at the Planned Parenthood facility in your community as we protest and pray for an end to Planned Parenthood's massive government subsidy, and an end to abortion in our country."
"Patients don't go to Planned Parenthood health centres to make a political statement -- they go to receive quality care from a provider they know and trust," Carter said in a statement.
Planned Parenthood supporters also rallied on Saturday in a show of solidarity with the organisation, which provides a variety of health services including cancer screenings, HIV testing and STI/STD treatment as well as family planning, birth control and abortion.
Carter expressed gratitude for the counter-protests, though she cautioned in a statement against rallies being held immediately outside the organisation's health clinics.
Planned Parenthood serves more than 2.5 million patients each year in over 650 health centres across the country.
Abortions account for 3 percent of its services, according to the organizstion's annual report from October 1, 2013, to September 30, 2014.
However, US Federal law bars government funding from paying for abortion services except in cases where the woman's life is in danger or if the pregnancy is the result of incest or rape, ABC News reports.
Republican lawmakers have proposed bills to cut off public funding to any organisations that offer abortions, a move that Planned Parenthood supporters believe would threaten the availability of the organisation's health services to women.