Under a peace deal, the US would have withdrawn its troops mainly in exchange for Taliban assurances that it will not allow Afghanistan to become a haven for terrorist groups like al-Qaeda and the Islamic State (ISIS/ISIL).
The assault came days after the top USA peace negotiator, Zalmay Khalilzad, proclaimed that almost a year of peace negotiations with the Taliban had yielded a deal "in principle".
US news outlets reported that Pence and the administration's national security adviser, John Bolton, internally at the White House voiced objections to holding the meeting at Camp David.
September 11 marks the 18th anniversary of the attack by Al-Qaeda on World Trade Center in NY in 2001.
About 14,000 USA troops remain in Afghanistan to train local forces.
"If Trump wants to stop talks, we will take the first way and they will soon regret it".
A White House meeting with the Taliban would have been "a step too far", said Trump, adding that he thought "Camp David would be good, and I still do".
However then on Saturday, Trump revealed that he had cancelled an unprecedented assembly between the Taliban and himself at storied Camp David.
Till this weekend, there had been steadily mounting expectations of a deal that may see the USA draw down troop ranges in Afghanistan.
'By way of advisers, I took my very own recommendation, ' he later instructed reporters. The government has been fighting the Taliban, which has been waging a war against Kabul for nearly two decades. Several called the timing unfortunate but the idea of talks worthwhile, a potential path toward peace for Afghans and Americans tired of Washington's longest war.
It is widely thought that Trump has been pushing for a withdrawal of United States troops in time for his 2020 reelection bid.
Nevertheless, whether or not due to final week's killing of a USA soldier, as he says, or on account of wider misgivings, that objective now seems in tatters. That, Khalilzad had said, was for the Afghans to work out with the Taliban.
Several Republican lawmakers concurred with the president's decision on the talks.
Senator Mitt Romney stated that "it would not have been my option to have the Taliban at Camp David" - an opinion echoed by Senator Ron Johnson, who stated he was "glad" the talks weren't held there. "While we certainly want that, there is so much more involved in the peace process", said Judd, who lost her partner, Christine Egan, in the attack on the World Trade Center.
Many young people, especially young women, are anxious about future restrictions to their participation in the socio-economic and political life of their country, he added.