President Donald Trump's decision to cancel Afghan peace talks will cost more American lives, the Taliban said on Sunday 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 after Trump unexpectedly canceled secret talks planned for Sunday with the Taliban's major leaders at the presidential compound in Camp David, Maryland. He broke off the talks on Saturday 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, criticized 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. "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 reduce US military support for Afghan troops until it was convinced the Taliban could follow through on 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."

Trump has long wanted to end US involvement in Afghanistan - since his days as a candidate - and American diplomats have been talking with Taliban representatives for months about a plan to withdraw thousands of US troops in exchange for security guarantees by the Taliban.

US and Taliban negotiators struck a draft peace deal last week that could have led to a drawdown of troops from America's longest war. There are currently 14,000 US forces as well as thousands of other NATO troops in the country.