A federal judge on Thursday blocked key provisions of a ­Florida law regulating groups that organize voter-registration drives, escalating a debate over newly restrictive voter-access laws that have become a major issue in the presidential campaign.

The decision by U.S. District Judge Robert L. Hinkle marked the first time a federal jurist has struck down provisions in one of the voting laws passed by nearly 20 states since last year. The laws are a flashpoint in President Obama’s battle for reelection, with his supporters saying they target minorities and other pro-Obama groups. Republicans say the measures are needed to combat voter fraud.