President Donald Trump's decision to cancel Afghan peace talks will cost more American lives, the Taliban said while the United States promised to keep up military pressure on the militants, in a stunning reversal of efforts to forge a deal ending nearly 20 years of war in Afghanistan.

The Islamist group issued a statement hours after Trump unexpectedly canceled planned secret talks with the Taliban's "major leaders" at the presidential compound in Camp David, Maryland. He broke off the talks after the Taliban claimed responsibility for an attack in Kabul last week that killed an American soldier and 11 others.

Zabihullah Mujahid, a Taliban spokesman, criticised Trump for calling off the dialogue and said US forces have been pounding Afghanistan with attacks at the same time.

"This will lead to more losses to the US," he said in a statement. "Its credibility will be affected, its anti-peace stance will be exposed to the world, losses to lives and assets will increase."

In Washington, Secretary of State Mike Pompeo said that Afghan peace talks were on hold and Washington would not withdraw troops from the region until it was convinced the Taliban could follow through on any significant commitments.

The United States has recalled US special envoy for Afghanistan Zalmay Khalilzad to chart the path forward, Pompeo said in appearances on Sunday TV news shows. Asked on "Fox News Sunday" whether Afghan talks were dead, Pompeo said, "For the time being they are."

The secret plans by Trump emphasised how much faith the US president puts on personal diplomacy, even with people previous heads of state would have avoided meeting for fear of granting them imprimatur – now apparently including members of a militant group the US government officially classifies as terrorists.