But Booker drew a new line on CNN Monday after Trump explicitly condemned white supremacy in a White House speech addressing the shooting in El Paso, Texas.
"Republicans and Democrats must come together and get strong background checks, perhaps marrying this legislation with desperately needed immigration reform", Mr. Trump tweeted.
Trump, who is scheduled to deliver public remarks later on Monday following the attacks, appeared to dismiss accusations following the two shootings in Texas and OH that his rhetoric has stoked racial hatred and provoked attacks amid a deepening political divide.
"Leader McConnell, do the right thing", Schumer said on Sunday. "These are people that are very, very seriously mentally ill". Three mass shootings this year - including the mosque killings in Christchurch, New Zealand - were announced on the website before they occurred.
A senior White House official declined to provide additional details, and did not signal whether Trump might endorse existing background check overhaul bills.
Trump's remark echoed Senate Judiciary Chairman Lindsey Graham, (R-SC), who earlier blamed mental illness for the El Paso rampage, while calling on every state to enact the Extreme Risk Protection Orders, commonly known as "Red Flag" laws, aimed at detecting individuals showing signs of mental distress and preventing them from obtaining weapons.
The suspect in the El Paso shooting is believed to be the author of an anti-immigrant manifesto.
Though he never got behind any specific legislation, Trump on that day urged lawmakers who have authored various bills to address school shootings and gun violence to consolidate their ideas in a single bill that he can sign into law.
Trump also highlighted the El Paso shooter's use of social media to publish his anti-immigrant manifesto, "The shooter in El Paso posted a manifesto online consumed by racist hate".
Article 370: Pakistan Expels Indian High Commissioner Ajay Bisaria, Suspends Trade
He said it prevented application of other Indian laws, including ones that protected minorities and established minimum wages. No permission has been granted this week for worldwide reporters to visit the region.
This isn't the first time the president has been vocal about expanding background checks in the wake of mass shooting events.
In February, the House approved bipartisan legislation to require federal background checks for all gun sales and transfers and legislation to allow a review period of up to 10 days for background checks on firearm purchases.
He claimed he would stand up to the gun lobby and finally get results in quelling gun violence.
Trump suggested Monday that a background check bill could be paired with his long-sought effort to toughen the nation's immigration system.
Trump, back at the White House after remaining largely out of view for two days at his New Jersey golf club, declared the shootings in Texas and OH barbaric crimes "against all humanity" and called for unity to respond to an epidemic of gun violence.
"Fake News has contributed greatly to the anger and rage that has built up over many years", he tweeted.
"A lot of good things are in the works", Trump said, adding that he would make a statement at 10:00am Monday.
On Saturday, several Mexican citizens were among the 21 people killed at a Walmart by a man who drove from his home in Allen, Texas, 660 miles (1,062 km) away, to El Paso, authorities said. "The president has made my community and my people the enemy".
On gun control, a majority of Americans have consistently said they support stronger laws, but proposals have stalled repeatedly in Congress, a marked contrast to some countries that have acted swiftly after mass shootings. "And maybe we can do something to begin dealing with gun laws in a rational way".