Although the Taliban said they would not monopolize power in the region, they insist that a peace deal will not be reached until a new government is negotiated.
While the Taliban is quickly gaining ground, CIA Director William Burns said that a collapse of the Afghan government wasn't inevitable.
The U.S.' airstrikes come as the Taliban has overrun roughly half of Afghanistan's 419 districts, U.S. Gen. Mark Milley said.
"A significant amount of territory has been seized over the course of six, eight, 10 months by the Taliban," Milley said.
Three rockets were fired at the presidential palace in a suspected Taliban attack, though no injuries were reported.
Erdogan acknowledged the Taliban had some "discomforts" over Turkey's proposal for Hamid Karzai International Airport.
The Taliban is now believed to control about half of the 400 provinces in the country.
Siddiqui and the Afghan officer were killed as fighting in the region over border crossings intensified.
After being rescued, Ahmad Shah said: "I did not surrender, I did not lay down my arms and I fought back."
"We're glad that they're doing what they're doing," a Defense Department official said of the Taliban fight against ISIS, "because it mirrors and parallels what we're trying to do for our counterterrorism mission."
Residents of the border town Chaman on the Pakistan side reported seeing the Taliban's signature white flag flying across the boundary line.
The former president said he believed the result will lead to "unspeakable harm" for Afghan women and girls from a potential return of the Taliban.
"We know that with that violence, it would be very difficult to achieve a political settlement," Miller told Taliban officials.
"The Taliban always had a saying: 'America has the watches but we have the time,'" said the congressman.
"It doesn't have to be that way and it's not like the Afghans are going to be doing this without our help," Pentagon spokesman John Kirby said.
Taliban fighters were greeted warmly by local residents after the taking of Islam Qala, according to a Taliban spokesman.
Mohammad Javad Zarif, the Iranian Foreign Minister, urged delegates to "take difficult decisions today for the future of their country."
Other countries have closed their consulates after a surge of Taliban victories in northern Afghanistan.
Hundreds of Afghan security personnel were reportedly forced to retreat into Tajikistan over the weekend after Taliban fighters advanced in Northern Afghanistan.
A Pentagon official said on Friday that American and NATO troops had departed the key military stronghold, 30 miles from Kabul.
Miller gave a sobering assessment of the country's deteriorating security situation as America winds down its so-called "forever war."
The Taliban may be aiming to claim Afghanistan's provincial capitals once U.S. military forces are withdrawn by Sept. 11, U.N. special envoy for Afghanistan Deborah Lyons said.
"We deplore this unfair combination that is contrary to justice and international law," the Hamas website stated.
As John Quincy Adams noted, we should not go abroad in search of monsters to destroy.
The congresswoman said she was discussing "specific incidents" and not making a "moral comparison between Hamas and the Taliban and the U.S. and Israel."
The statement from the House members came after Omar seemed to compare the U.S. to Hamas and the Taliban.
Congressional lawmakers raised concerns with Washington's special envoy to Afghanistan in hearings this week about the future of the war-torn country with a resurgent Taliban and U.S. troops withdrawn.
At least 50 people have died and more than 100 have been injured in the May 8 bombings, though an expert at the U.S. Institute of Peace said those numbers are likely to tick higher.
Hours after the Taliban announced a cease-fire, 11 bus passengers died and at least 24 were wounded in a roadside bombing.