Senior Democrats have reached agreement with the National Rifle Association on what could be the first federal gun-control legislation since 1994, a measure to significantly strengthen the national system that checks the backgrounds of gun buyers.

The sensitive talks began in April, days after a mentally ill gunman killed 32 students and teachers at Virginia Tech University. The shooter, Seung Hui Cho, had been judicially ordered to submit to a psychiatric evaluation, which should have disqualified him from buying handguns. But the state of Virginia never forwarded that information to the federal National Instant Check System (NICS), and the massacre exposed a loophole in the 13-year-old background-check program.