Trump has been criticized for failing to push for tougher gun control measures during his Monday address to the nation and instead pivoted to mental health issues and blaming video games and social media for gun violence.
The president's opponents say he and his Republican Party are in the pocket of the influential gun lobby.
The shootings have also brought the president's crackdown on migration and language toward migrants into focus. Trump has used the term "invasion" to describe flows of Central Americans trying to enter the US and called for four non-white female members of Congress - all US citizens - to "go back" to the countries "from which they came."
The 21-year-old shooter in El Paso posted an anti-migrant, white supremacist screed online before going on a rampage at a supermarket, killing 22 people. He was captured alive by police.
The motive of the 24-year-old Dayton shooter remains unclear. He was killed by law enforcement officers at the scene of the crime, outside a bar.
Dayton Mayor Nan Whaley, a Democrat, said she was "disappointed" with Trump's address to the nation, saying it failed to adequately address issued around gun control. She said the president has so far been "unhelpful."
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