Hillary Clinton has accused Republican rival Donald Trump of helping Islamic State militants recruit more fighters.
Mr Trump, meanwhile, said Mrs Clinton's "weakness" while Democratic President Barack Obama's secretary of state had emboldened terrorists worldwide to attack the United States.
Both US presidential candidates tried to use the bomb blasts in New York and New Jersey to flex their national security credentials, as world leaders were gathering in security-heightened New York for the annual United Nations General Assembly.
Mr Clinton said Mr Trump's rhetoric against what he calls "radical Islamic terrorism" is helping Islamic State, also known by the acronym ISIS.
"We know that a lot of the rhetoric we've heard from Donald Trump has been seized on by terrorists, in particular ISIS, because they are looking to make this into a war against Islam rather than a war against jihadists," she told reporters in White Plains, New York.
The Trump campaign responded by saying Clinton bears some responsibility for the violence by not persuading Obama to leave a residual force of US troops in Iraq when she was his secretary of state from 2009 to 2013.
President Obama and the Iraqi government failed to reach agreement at the end of 2011 on extending a US-Iraqi status of forces agreement, and most American troops were withdrawn.
The Republican candidate has sought to tie Clinton to the decisions of the Obama administration.
"Hillary Clinton's weakness while she was secretary of state has emboldened terrorists all over the world to attack the US, even on our own soil. They are hoping and praying that Hillary Clinton becomes president so that they can continue their savagery and murder," Mr Trump said on Facebook. He did not give specifics.
The campaigns weighed in after the weekend of bomb incidents and multiple stabbings in central Minnesota as the 8 November election loomed closer.
Throughout much of the last year Mr Trump has called for a ban on Muslims entering the United States. The US Constitution guarantees freedom of religion.
On 31 August 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."
At a speech in Philadelphia on Monday, Clinton called for vigilance.
"This is a fast-moving situation and a sobering reminder that we need steady leadership in a dangerous world," she said.
The renewed focus on terrorism came as the presidential rivals prepared for their first debate next Monday at Hofstra University in Hempstead, New York, east of the city.
Mr 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."