FORT LAUDERDALE, Fla. — The scrutiny after the mass shooting at a high school in Parkland, Fla., immediately fell on law enforcement’s failures to heed warnings about the confessed gunman’s troubling behavior and prevent him from carrying out his deadly rampage. It took weeks for the focus to turn in earnest on the shortcomings of another level of government that knew Nikolas Cruz well: the Broward County Public Schools.

And now the parents of two 14-year-old students who were among those killed at Marjory Stoneman Douglas High School have concluded that the best way to fix what they think went wrong — and to prevent another massacre from ever taking place — is to run for the school board themselves.

Lori Alhadeff, who lost her daughter, Alyssa, and Ryan Petty, who lost his daughter, Alaina, announced their candidacies side-by-side on Tuesday, pledging to hold the district accountable for making its schools safe. Their campaigns are a direct response to lingering questions about whether the district could have done more to stop Mr. Cruz, a former student, from killing 17 students and educators in February.

“Like many of the families, we’ve dedicated ourselves to changing the system that would allow someone like Nikolas Cruz to slip through the cracks,” Mr. Petty, a telecom executive, said at a news conference outside the Broward County Governmental Center shortly after he and Ms. Alhadeff filed for the Aug. 28 election.