The so-called notice of intent to file a claim is required by Florida law before a lawsuit can be brought against government entities.
The minimum age for handguns nationally is already 21. But a person can be as young as 18 to buy a rifle in Florida, with no waiting period.
Trump had last week said he wanted to raise the legal minimum age for buying an assault rifle to 21.
Deputy Scot Peterson was the only law enforcement officer present on 14 February when the rampage started, Broward County Sheriff Scott Israel said.
The US Constitution’s Second Amendment protects the right to bear arms.
Trump made the comment during an emotional hour-long White House meeting with students who survived the Florida shooting and a parent whose child did not.
On Tuesday the Republican-controlled Florida House of Representatives rebuffed a bid to bring up a bill to block sales of assault-style rifles in the state.
He accused his Democratic predecessor, Barack Obama, of failing to do enough to stop Russian election interference.
Authorities said Nikolas Cruz stopped at a Wal-Mart, a Subway restaurant and a McDonald’s immediately after carrying out the second-deadliest mass shooting at a public school in US history.
The ex-student, identified as Nikolas Cruz, 19, walked into the Marjory Stoneman Douglas High School in Parkland shortly before classes ended and opened fire on students and teachers.
The violence erupted shortly before dismissal at Marjory Stoneman Douglas High School in Parkland, a placid, middle-class community about 72 km north of Miami.
Security was beefed up as millions of people turned out for the Gay Pride Parades across the US.
An acquaintance says the Orlando nightclub shooter appeared agitated before the attack.
US Democrats and Republicans nearly came to blows over gun control legislation.
Gun control laws have intensified pressure on lawmakers, who moved to take the issue to the Senate floor.
The gunman in the Orlando gay night club track used a semiautomatic rifle that would have been banned.
Trump made similar comments last year, about the targeting of specific demographic groups for extra scrutiny.
Donald Trump has drawn criticism from many in his party for his comments on American Muslims.
