Cheney said that, contrary to Secretary of State Mike Pompeo's claims, there is no verification mechanism provided in the agreement to ensure the Taliban keeps its promises.
The Taliban's spokesman in Qatar, Suhail Shaheen, said in a tweet after the U.S. strike on Wednesday that the insurgent group had implemented "all parts of the agreement one after the other to prevent escalation."
Taliban commander Salih Khan in Helmand, meanwhile, told CBS News' Sami Yousafzai that the deal with the U.S. could "vanish" if American forces continue targeting Taliban fighters. He said he was awaiting further word from the group's leadership, but that he had already received orders to resume attacking Afghan forces — but not foreign troops.
"Now we are happy to resume attacking U.S. forces as well, if our leaders order" it, he said.
Another Taliban representative in Qatar, Salam Hanafi, told fellow leaders of the group in a message forwarded to CBS News' Yousafzai later Wednesday that the Taliban did not consider the American airstrike a violation of the deal signed over the weekend. Hanafi said that under the deal U.S. forces can still defend their Afghan allies from attacking Taliban militants, "just on the spot" of the initial attack.
He said as long as American troops do not pursue or carry out targeted strikes against the insurgents elsewhere, retaliation was essentially fair game.
"If [the] USA did not add this condition, then [the] Afghan government would collapse, instead of in 14 months, in 14 days," Hanafi boasted. The group has long been dismissive of the Afghan government, and insisted on carrying out negotiations for the agreement signed in Doha with U.S. diplomats, not Afghan government officials.
Javid Faisal, a spokesperson for Afghanistan's National Security Adviser, told CBS News that since the end of the official one-week Reduction in Violence that precipitated the signing of the peace agreement, the Taliban had conducted 76 attacks across the country. He said 85 Taliban militants were killed in retaliation.
The U.S. deal with the Taliban was only designed to halt the fight between the militants and the foreign forces in Afghanistan, and it was widely expected that after that initial week-long Reduction in Violence, the Taliban would continue attacking Afghan forces until the insurgents reach a final agreement with the Afghan government.
Those intra-Afghan negotiations are scheduled to begin on March 10, as laid out in the agreement signed in Doha. However, the Taliban are demanding a prisoner swap to have 5,000 militants freed in exchange for 1,000 Afghan security forces held by the group before intra-Afghan talks even begin.