President Donald Trump said this weekend that he canceled a planned meeting with Taliban leaders at Camp David because of a recent Taliban attack that killed a US service member and several others in Afghanistan.

But the Taliban is telling a different story, saying the meeting was canceled because the insurgent group believed the US was trying to trick them into "political suicide," The New York Times reported.

The report said Trump originally planned to fly Taliban leaders as well as Ashraf Ghani, the president of Afghanistan, to Camp David, hold meetings with each side, and make a "grand announcement" once a deal had been reached to begin withdrawing US troops from Afghanistan.

But the Taliban pushed back, with one official telling The Times, "If Trump and his administration think they would solve the confrontation between the government and the Taliban somewhere in Washington in a meeting, that's not possible because we do not recognize the stooge government."

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President Donald Trump and the Taliban appear to be telling two different stories about why he canceled a planned meeting with the group's leaders at Camp David that was originally set to take place Sunday.

Trump said he called off the meeting and any other peace negotiations due to a recent Taliban attack that killed a US service member and several others in Afghanistan.

The president went on to say that if the Taliban cannot agree to a ceasefire during the talks "and would even kill 12 innocent people, then they probably don't have the power to negotiate in a meaningful agreement anyway."

But The New York Times reported on Sunday that the meeting's cancellation had more to do with the Taliban's resistance to the US's terms on a potential peace deal that would have seen 5,000 US troops withdraw from five bases in Afghanistan within 135 days.

According to the report, Trump originally planned to fly Taliban leaders and Ashraf Ghani, the president of Afghanistan, to Camp David, hold meetings with each side, and make a "grand announcement" once a deal had been reached.

Read more: 'He's losing his s---': Trump's advisers are increasingly worried about his mental state following days of erratic behavior

But Taliban leaders reportedly believed the Americans were trying to trick them into "political suicide" and that the US was rushing to finalize certain issues related to the potential peace deal.