Writing on Twitter, Mr Trump said he had been due to meet both members of the militant Islamist group and the president of Afghanistan at the presidential retreat in Maryland on Sunday.
However, he announced he had decided to call off the negotiations after the Taliban claimed credit for a car bomb in Kabul earlier this week, which left 12 dead, including one US soldier.
“Unbeknownst to almost everyone, the major Taliban leaders and, separately, the President of Afghanistan, were going to secretly meet with me at Camp David on Sunday,” Mr Trump wrote.
“They were coming to the United States tonight. Unfortunately, in order to build false leverage, they admitted to an attack in Kabul that killed one of our great great soldiers, and 11 other people.
“I immediately cancelled the meeting and called off peace negotiations. What kind of people would kill so many in order to seemingly strengthen their bargaining position?”
The president added: “If they cannot agree to a ceasefire during these very important peace talks, and would even kill 12 innocent people, then they probably don’t have the power to negotiate a meaningful agreement anyway. How many more decades are they willing to fight?”
Mr Trump’s decision to pull out of talks came just days after the US’s top negotiator for peace in Afghanistan, Zalmay Khalilzad, said the two sides were close to a deal to end America’s longest war..
A draft framework agreement had been drawn up under which US troops would leave five military bases in Afghanistan within 135 days of the signing of the pact.
In return, the Taliban would be expected to guarantee the country will not be used as a launchpad for global terrorist operations.
However, the Taliban has carried out several deadly attacks across Afghanistan in recent weeks while talks with US envoys have been ongoing.
The attacks are seen as strengthening the negotiating position of the Taliban, who control or hold sway over roughly half of Afghanistan and are at their strongest since their 2001 defeat by a US-led invasion.
But some critics have warned the Taliban was merely waiting out the US and that another American goal in the talks, a ceasefire, will probably not happen as foreign troops leave.
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