The two Democratic leaders pointed to Trump's support for Rep. Greg Gianforte (R-Mont.), who pleaded guilty to assaulting a reporter, and accused the president of supporting "dictators around the world who murder their own citizens, and referring to the free press as the enemy of the people."
President Trump's words ring hollow until he reverses his statements that condone acts of violence," Schumer and Pelosi said.
Their statement comes after Trump said that he condemned "political violence" and urged the country to unify after suspicious packages were mailed to a number of prominent Democratic officials, donors and to CNN, a network often targeted by Trump.
"I just want to tell you that in these times, we have to unify. We have to come together and send one very clear, strong, unmistakable message that acts or threats of political violence of any kind have no place in the United States of America," Trump said at a White House event where he signed an anti-opioid epidemic bill into law.
Authorities intercepted explosive devices addressed to former President Obama, Hillary Clinton, former CIA Director John Brennan and former Attorney General Eric Holder. Another suspicious package addressed to Rep. Maxine Waters (D-Calif.) was also intercepted by police.
On Monday an explosive was found at Democratic mega-donor George Soros's home. And separately on Wednesday, the Time Warner building in New York City was evacuated after reports of a suspicious package sent to CNN.
Trump did not mention any of the officials targeted by name and did not address criticism that his own rhetoric has helped contribute to the political environment.
Republican and Democratic lawmakers have condemned the threats, but some of the president's critics have noted that his comment on Wednesday comes just days after he praised Gianforte at a rally in Montana.
Schumer and Pelosi added that they "listened with great interest" to the president's comments on Wednesday.
"Once again, we salute the heroism of America's first responders as they work to counter the outrageous mail bomb attack. ... We all take an oath to support and defend the Constitution and protect the American people, and that is our first responsibility," they said.
The joint statement comes after Schumer said in a tweet on Tuesday that political violence should be condemned regardless of who is being targeted.
"Make no mistake: Despicable acts of violence and harassment are being carried out by radicals across the political spectrum - not just by one side. Regardless of who is responsible, these acts are wrong and must be condemned by Democrats and Republicans alike. Period," Schumer said.
His tweet included screenshots of a CNN article about GOP Rep. Kevin McCarthy's (Calif.) office being vandalized and the explosive device being discovered at Soros's home.
