Both Clinton and Trump tried to use the attacks to flex their national security credentials, with world leaders gathering in security-heightened New York for the annual United Nations General Assembly.
Speaking to reporters in White Plains, New York, Clinton urged Americans to remain calm but vigilant.
In a statement, Trump's campaign accused the White House of playing down the threat posed by Islamic State.
The campaigns weighed in after the weekend of bomb incidents and multiple stabbings in central Minnesota as the Nov. 8 election loomed closer.
In the most serious incident, a bomb went off in New York City's Chelsea neighborhood on Saturday, injuring 29 people; another explosive device was found nearby. Earlier that day, a pipe bomb went off in Seaside Park, New Jersey, further south of the city.
On Sunday night, as many as six explosive devices were found in Elizabeth, New Jersey, just west of New York.
The incidents, just days after the 15th anniversary of the Sept. 11, 2001, attacks, put the United States' most populous city on edge.
In another incident, a man stabbed nine people at a central Minnesota mall on Saturday before being shot dead by an off-duty policeman. On Sunday, Islamic State claimed responsibility, calling the man "a soldier," and the FBI said it was investigating the attack as a potential act of terrorism. Reuters could not verify the claim of responsibility.
Clinton cited comments from former U.S. intelligence director Michael Hayden in saying that Islamic State militants were using Trump's rhetoric to attract fighters. She cited Hayden as saying that her opponent was a recruiting sergeant for terrorists.
Trump throughout much of the last year has called for a ban on Muslims entering the United States.
On Aug. 31, he said, that, if elected, he would suspend immigration from "places like Syria and Libya" and would order a list of regions and countries be drawn up from which "immigration must be suspended until proven and effective vetting mechanisms can be put into place."
Clinton said Trump's words are helping Islamic State because they want to recruit more fighters to their cause by "turning it into a religious conflict. ... They are attempting to make this into a war against Islam," she said.
The renewed focus on terrorism came as Clinton and Trump prepare for their first debate next Monday at Hofstra University in Hempstead, New York.
The Trump campaign responded to Clinton's attack by saying she bears some responsibility for the violence by not persuading Democratic President Barack Obama to leave a residual force of U.S. troops in Iraq when she was his secretary of state.
Obama failed to reach agreement with the Iraqi government at the end of 2011 on extending a U.S.-Iraqi status of forces agreement, and most American troops were withdrawn.
Trump has sought to tie Clinton to the decisions of the Obama administration, pointing to the four years she was secretary of state from 2009 to 2013.
"Hillary Clinton’s comments today accusing Mr. Trump of treason are not only beyond the pale, it’s also an attempt to distract from her horrible record on ISIS. If Clinton really wants to find the real cause of ISIS, she needs to take a long, hard look in the mirror," Trump campaign spokesman Jason Miller said.
A U.S.-led coalition has been fighting ISIS, an acronym for Islamic State, mainly through air strikes in Syria and Iraq.
Obama was in New York on Monday to attend the United Nations General Assembly and meet world leaders.
Trump, who has based much of his campaign message on arguing that the United States is no longer safe and that he alone can protect the nation, told Fox News on Monday morning that he expects more attacks.
"I think this is something that maybe will ... happen more and more all over the country," Trump told Fox News.
Asked if he was saying there would be more attacks, he replied, "Yeah, because we've been weak. Our country's been weak."
(Additional reporting by Ginger Gibson, Alana Wise and Emily Stephenson in Washington, writing by Steve Holland; Editing by Jonathan Oatis)
