"Any peace agreement which denies the USA a robust counterterrorism capability in Afghanistan is not a peace deal", Graham said. The U.S. envoy in the talks, Zalmay Khalilzad, said Sunday that the peace process must be accelerated, including holding talks between the Taliban and the Afghan government and other Afghans.
Officials on August 16 said Trump was meeting with his top advisers to review negotiations with the extremist group about a possible US troop pullout from war-ravaged Afghanistan and the potential for a political settlement in the almost 18-year conflict.
Trump has complained that USA forces in Afghanistan serve as "policemen".
Both sides had raised expectations of being close to finalising an agreement prior to convening the latest round of talks. Nobody took responsibility of the attack and Pakistan officials only said that an improvised explosive device (IED) was planted inside the building.
"Share President Trump's "hope" that we can honorably end the war in Afghanistan with the Taliban".
Assuming the talks continue as outlined, discussions between the Afghan sides would also consider the extent to which the United States military could maintain a residual counterterrorism presence in Afghanistan, something that many in the administration, and Congress, believe is imperative. The US wants to withdraw thousands of troops and turn the page on its longest ever war.
The US defence official, however, said differences remained over US demands that the insurgents publicly renounce ties to al Qaeda and other militant groups and agree to a nationwide ceasefire, the official said.
Taliban officials say the killing of the brother of their leader in a bomb attack won't derail talks with the United States aimed at securing the withdrawal of U.S. troops after 18 years of war.
A day after the warning, a Taliban vehicle bomb targeting Afghan security forces killed 14 people and wounded more than 140, mostly children, women and other civilians.
For years, the Taliban has refused to meet with Afghan officials, denouncing them as United States puppets.
In public statements, Ghani - running for a new term - has rejected any delay, and last week said the vote was "vital" to the nation.
Hering is a retired Navy vice admiral and a fellow at the American College of National Security Leaders. Others among the 16 candidates challenging Ghani have said the election must be delayed whether or not a viable agreement is announced.
Graham insists the USA should maintain a counterterrorism force inside Afghanistan, even if a deal is reached with the Taliban. Both the Taliban and a local affiliate of the Islamic State group carry out bloody attacks in the capital.
Pompeo released a statement after the meeting that touched on Graham's concern. "To trust the Taliban to control Al Qaeda" and other militant groups in Afghanistan "as a replacement for a U.S. counterterrorism force would be a bigger mistake than Obama's Iranian nuclear deal, " he said.