Almost immediately after the remarks, the Taliban launched an offensive to retake the Yangi Qala district in the northern province. Security forces killed 28 Taliban fighters, including a commander, and the Afghan government has sent reinforcements to counter Taliban militants.
The insurgent group responded to Trump's remarks with criticism and a threat.
"We had two ways to end occupation in Afghanistan, one was jihad and fighting, the other was talks and negotiations," Taliban spokesman Zabihullah Mujahid said. "If Trump wants to stop talks, we will take the first way and they will soon regret it."
Afghan President Ashraf Ghani called for peace and asked the Taliban to agree to a cease-fire. The plan had been for Ghani and Taliban negotiators to meet with Trump at Camp David, the presidential retreat in Maryland.
Trump canceled the meeting Sunday after the Taliban claimed responsibility for a suicide bombing in Kabul that killed 12 people, including a U.S. soldier. The president said he decided to cancel the meeting and lashed out at the Taliban, saying they killed to "strengthen their bargaining position."
Taliban and U.S. negotiators have been trying for a peace settlement for months, which would result in a total withdrawal of U.S. forces from the Middle Eastern nation, where they've been since late 2001. Monday, Trump said those negotiations are over.
"They're dead," he said. "As far as I'm concerned, they're dead."
Some questioned the idea of hosting Taliban officials in the United States so close to the 18th Sept. 11, 2001, anniversary.
"I always think it is good to meet and talk, but in this case I decided not to," Trump tweeted.
About 14,000 U.S. troops remain in Afghanistan to train local forces.