Donald Trump vowed to hit the Taliban "harder than ever" as the United States marked the 18th anniversary of the September 11, 2001 terrorist attacks that led to its longest war in Afghanistan.
The US president also blamed the Taliban for the abrupt cancellation of planned peace talks at Camp David, which followed the death of a US soldier in a suicide car bombing in Kabul last week.
Speaking at the Pentagon, where he was marking the anniversary, Mr Trump said: "We had peace talks scheduled a few days ago. I called them off when I learned they had killed a great American soldier from Puerto Rico and 11 other innocent people.
"They thought they would use this attack to show strength, but actually what they showed is unrelenting weakness. The last four days. We have hit our enemy harder than they have ever been hit before, and that will continue."
The US president added: "If, for any reason, they come back to our country, we will go wherever they are, and use power, the likes of which the United States has never used before."
Mr Trump said he was "not talking about nuclear power" but the Taliban "will never have seen anything like what will happen to them."
He added: "No enemy on Earth can match the overwhelming strength, skill and might of the American armed forces."
Later, speaking at the White House, Mr Trump repeated his assertion that talks with the Taliban were "dead".
He said: "What they did was horrible, they killed an American soldier. I said that's the end of them, get them out, and we're hitting them very hard. That was my decision. We are hitting the Taliban harder than they've ever been hit."
For nearly a year Zalmay Khalilzad, the US envoy, has been negotiating with the Taliban on issues including a US troop withdrawal from Afghanistan, and Taliban guarantees to keep the country from again being used as a launch pad for global terror attacks.
There were fears Mr Trump's cancellation of the negotiations could bring more carnage in Afghanistan.
Mr Trump has said he wants to withdraw around 5,000 of the 14,000 US military personnel still in the country.
In New York relatives of victims, survivors, police officers, firefighters and city leaders marked the anniversary of the terrorist attacks with a ceremony at Ground Zero, where planes hijacked by al-Qaeda crashed into the World Trade Center.
Relatives read out the long list of those who were killed, and held placards with images of their loved ones.