Trump, who is scheduled to address the nation following the shootings in Texas and Ohio, said the victims' deaths could not be "in vain" and called on both Republicans and Democrats to take steps to require further screenings for gun buyers.
"We cannot let those killed in El Paso, Texas, and Dayton, Ohio, die in vain. Likewise for those so seriously wounded. We can never forget them, and those many who came before them," Trump tweeted ahead of his White House address.
The President also suggested tying immigration reform to strengthening background checks.
"Republicans and Democrats must come together and get strong background checks, perhaps marrying this legislation with desperately needed immigration reform. We must have something good, if not great, come out of these two tragic events!"
On Saturday, a gunman killed 20 people at a Walmart store in El Paso, Texas, in what officials said appeared to be a racially-motivated hate crime.
Later, another gunman in Dayton, Ohio, killed nine people. Dozens were also wounded in both shootings.
Trump also suggested that the media was responsible for the scourge of mass shootings and "the anger and rage that has built up over many years".
Senator Kirsten Gillibrand, a New York Democrat who is also seeking her party's 2020 presidential nomination, said that it was "absurd" for Trump to link immigration and gun violence together.
"He's linking the issue of basic, common-sense gun reform, that we should be going back into the Senate to vote on, with this issue of immigration because again he continues to try to demonize people seeking asylum, people needing our help," she said.
( With inputs from IANS )