With the US military evacuation from Afghanistan completed a week ago, private groups are working to help those in the war-torn country still trying to get out.

About 1,000 people, including Americans, have been waiting in Afghanistan for clearance for their six privately chartered flights to leave, an organizer told Reuters, blaming the delay on the US State Department.

The organizer said the State Department did not tell the Taliban of its approval for flight departures from the international airport in the northern city of Mazar-i-Sharif — about 260 miles north of the capital Kabul — or provide a landing site.

"They need to be held accountable for putting these people's lives in danger," said the organizer, who asked for anonymity.

A US official, also speaking on condition of anonymity, said the US government "has not confirmed any Americans are in Mazar-i-Sharif trying to leave from the airport".

Asked about charter flights, a State Department spokesperson stressed that the US did not have personnel on the ground and therefore could not confirm details of the charter flights.

That includes verifying the number of American citizens and others on board, the accuracy of the manifest or "where they plan to land, among many other issues".

The spokesperson added, "We will hold the Taliban to its pledge to let people freely depart Afghanistan."

The passengers were waiting to board planes chartered by Mercury One, a charity founded by conservative media host Glenn Beck, newsweek.com reported.

Three other flights — two on a plane chartered by international development organization Sayara, and one by Goldbelt Inc, an Alaska Native corporation — also were grounded by the Taliban, awaiting clearance.

According to a second senior NGO official, Sayara plans to carry 700 passengers, at least 19 of whom are Americans, Newsweek reported.

The Mercury One rescue mission chartered two Airbus 340s and four Boeing 737s from Kam Air, the largest private Afghan airline, for eight evacuation flights to a Gulf state. The other three flights also were chartered from Kam Air, but their destination was unclear, the website reported.

Negotiations between the Taliban and State Department have been "stuck at this point" so the Taliban has not "granted final clearance" for the flights, the second official said US Representative Michael McCaul, a Texas Republican on the House Foreign Affairs Committee, called the developments a "hostage situation".

"We have six airplanes at Mazar Sharif Airport, six airplanes with American citizens on them as I speak, also with these interpreters, and the Taliban is holding them hostage for demands right now," McCaul told Fox News Sunday.

Eric Montalvo, a former US Marine Corps officer and a lawyer working with groups that chartered two of the six planes, told The Guardian: "The Taliban is not holding these planes hostage. The problem is the US government. All the State Department has to do is make a phone call, and these people will be able to leave immediately."

Both NGO officials disputed the "hostage'" depiction but told Newsweek that the passengers include at least 142 Americans.

"The planes are currently empty, and its passengers are still waiting in their safe houses for clearance for takeoff from the Taliban," the first NGO official told Newsweek. "I have more than 1,000 people on the master manifest that want to fly, of which 123 are Americans and the rest are special immigration visas."

In a series of Twitter posts Monday, US Senator Richard Blumenthal, a Connecticut Democrat, said he was "deeply frustrated" with the evacuation process.

"My staff & I have worked night & day to secure the safe passage of two planes waiting in Mazar-e Sharif to take American citizens, at-risk Afghan allies, & their families to safety," he wrote.

"I have been deeply frustrated, even furious, at our government's delay & inaction. There will be plenty of time to seek accountability for the inexcusable bureaucratic red tape that stranded so many of our Afghan allies," Blumenthal wrote.

The evacuation flights cost the Mercury One charity $750,000 each, the first NGO official told Newsweek. Mercury One reportedly raised more than $28 million to help evacuate Christians and other religious minorities from Afghanistan.

Meanwhile, the State Department said it "facilitated the safe departure" of four US citizens from Afghanistan on Monday, noting that the Taliban "was aware" and did not interfere in the evacuation.

A senior State Department official said the evacuation was done "by overland route from Afghanistan. "

US Representative Markwayne Mullin, an Oklahoma Republican, announced Monday that he helped the four safely leave Afghanistan.

"A little over three weeks ago, I received an email from a friend asking if there was anything we could do to help a young lady named Mariam and her 3 small children (all American citizens) get out of Afghanistan," he tweeted.

"Mariam had gone to visit her parents for the first time with the kids and became trapped in Kabul when the Taliban overran the city. We left two weeks ago today to get her, the children, and others out."

Mullin wrote that "despite the many frustrating setbacks" … at 05:32EDT they got out of Afghanistan".

Mullin called it a "flat out lie" that the State Department facilitated the evacuation, saying a "team of patriots … worked around the clock for two weeks to get them out, despite the many roadblocks from the State Department."

Reuters contributed to this story.