On Friday, the protesters started from various points in the city, converged on a downtown roundabout and walked to the home of the Deputy Prime Minister, but they were stopped some distance away from the residence by a heavy police presence.
Protesters were attacked with firecrackers by far-right groups, but police contained the confrontation, said Warsaw police spokesman Sylwester Marczak.
"There was aggressive behaviour on the part of soccer pseudo-fans (soccer hooligans) and also between the two sides, that's why police prevention units took action," Marczak said. He described the overall protest as "very peaceful considering the number of participants".
Noisy but disciplined marches were also held in other cities. More protests are planned next week.
Poland's constitutional court has preserved the provisions of the country's 1993 abortion law, one of Europe's strictest, that permit abortions when a pregnancy threatens a woman's health or results from rape or incest.