Mrs. Clinton did not use that phrase or respond directly to Mr. Trump’s broadsides. Her campaign instead sought to use the event to diminish their Republican rival. “This act of terror is the largest mass shooting in American history and a tragedy that requires a serious response,” Jennifer Palmieri, Mrs. Clinton’s communications director said, adding that: “Donald Trump put out political attacks, weak platitudes and self-congratulations.”

Mrs. Clinton, the presumptive Democratic presidential nominee, initially responded with caution Sunday morning after early reports about the assault, offering her thoughts to those affected “as we wait for more information.” But after President Obama spoke in the afternoon, and called the Orlando killings an “act of terror,” she issued a longer statement echoing the president. “This was an act of terror,” Mrs. Clinton said.

In her statement, Mrs. Clinton said “we need to redouble our efforts to defend our country from threats at home and abroad,” focusing on the threat of terrorism. Further down in her statement, she called for more stringent restrictions on guns.

“Finally, we need to keep guns like the ones used last night out of the hands of terrorists or other violent criminals,” she said, taking up the call many on the left made in the hours after the attack. Mr. Trump, who made no mention of access to firearms in any of his comments, said Mr. Obama should resign for his own refusal to say “radical Islam.”