HERNDON, Va. — Donald J. Trump on Monday called for strengthening the nation’s defenses against cyberattacks, saying that as president he would create a joint law enforcement task force to handle both cybersecurity as well as offensive cyberwarfare.

“Cyberattacks from foreign governments — especially China, Russia, North Korea, along with nonstate terrorist actors and organized criminal groups — constitute one of our most critical national security concerns,” Mr. Trump told a group of retired military veterans on Monday. “The scope of our cybersecurity problem is enormous. Our government, our businesses, our trade secrets and our citizens — most sensitive information — are all facing constant cyberattacks and reviews by the enemy.”

Mr. Trump, who once suggested that Russia hack Hillary Clinton’s emails, also stressed the importance of being able to wage “crippling” cyberattacks against the nation’s adversaries, calling it “the warfare of the future.” “We should turn cyberwarfare into one of our greatest weapons against the terrorists.”

Mr. Trump’s remarks came after a damaging week of largely self-inflicted missteps, underscored by a drop in many polls, which began last Monday with a shaky debate performance against Mrs. Clinton and went on to include a late-night Twitter rant against Alicia Machado, a former Miss Universe who is Hispanic.