Opting for a plan the administration officials described as "pragmatic," Trump backs legislation proposed in Congress aimed at providing more data for the background check system - a database of people who are not legally allowed to buy guns.
More contentious proposals, such as raising the minimum age for buying guns to 21 from 18, or requiring background checks for guns bought at gun shows or on the internet, will be studied by a commission headed by Education Secretary Betsy DeVos, the officials said.
The Justice Department will also provide an unspecified amount of grants to states that want to train teachers to carry guns in school an idea already in place in a small number of states, and backed by the National Rifle Association gun rights lobby.
Trump has said he believes armed teachers would deter school shootings and better protect students when they happen.
The president, who championed gun rights during his 2016 campaign, vowed to take action to prevent school shootings after a gunman killed 17 people at a high school in Parkland, Florida, on Feb. 14.
The shooting reignited the national debate over gun control. Students who survived the attack have pressured politicians to crack down on guns, and plan a march in Washington on March 24.
Senate Democratic leader Chuck Schumer called Trump's plan "tiny baby steps designed not to upset the NRA" and said Democratic senators would push for broader measures.
Trump met with the NRA privately at the White House twice last month as he weighed his response to the shooting - including the day after an unusual televised meeting where he chided lawmakers for being afraid of the group and challenged them to develop comprehensive legislation.
At that meeting, Trump embraced suggestions to close loopholes for gun buyers seeking to avoid the background check system, raise the age limit for buying rifles, and find ways to temporarily seize guns from people reported to be dangerous.
Trump has now embraced a proposal from John Cornyn of Texas, the No. 2 Senate Republican, and Democratic Senator Chris Murphy of Connecticut, which is supported by many but not all Republicans.
"We believe this legislation is important, is useful in improving the background check system - and can pass virtually immediately if there is not obstruction in Congress," a senior administration official said on a conference call.
Trump will call on state governments to allow law enforcement officials to obtain court orders to temporarily seize guns from people reported to be dangerous, officials said.
The administration will provide technical help to state governments looking to pass those laws.
Trump vowed to address mental health issues after the shooting, but his administration's recommendations for reforms included no concrete details, other than reviewing health and education privacy laws.
It will be up to the commission led by DeVos to study an assortment of other ideas, such as rating systems for violent entertainment, best practices for school buildings and security, and ideas for improving mental health services.
Trump has also backed a ban on "bump stocks," accessories that enable semi-automatic rifles to fire hundreds of rounds a minute. Bump stocks were used in the deadliest mass shooting in modern US history, which took place in October in Las Vegas.
On Saturday, the Department of Justice formally submitted a regulation to ban bump stocks that would not need congressional approval.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)