On Sunday, Emirates Flight EK640 and flydubai Flight FZ305 turned back to Dubai, after being unable to land at Kabul airport.
Evacuation flights are taking up most of the space at the airfield, as foreign diplomats leave the country.
The Taliban have taken over most of Afghanistan and the government is preparing to hand power over to them.
A flydubai representative said the airline had temporarily suspended flights.
"We will continue to monitor the situation and revise our plans in line with the directives from the authorities. We will be in touch with the passengers regarding their refund and rebooking options," they said.
The airline’s website showed a "forced return" on Sunday, while the Emirates website showed the status of its flight was "return, in flight".
Emirates flight EK640 was on approach to Kabul at Sunday lunchtime when it moved into a holding pattern, circling east of the Afghan capital several times. A holding pattern is a course flown while an aircraft awaits clearance to land.
The aircraft then turned back towards Pakistan and crossed the border, before setting a course for Dubai.
"Due to the unforeseen temporary closure of the runway at the time of Emirates’ approach at Hamid Karzai International Airport, Emirates Flight EK640 to Kabul operating on August 15 has returned back to Dubai," an Emirates airline representative said.
"We are monitoring developments around the situation in Afghanistan and are working closely with all the relevant authorities to ensure the safe operation of our services."
"Further updates on our operations to Kabul will be posted on emirates.com when available."
On Sunday night, Emirates said on its website that flights were suspended.
"Customers are advised that due to the developing situation in Afghanistan, all Emirates flights to/from Kabul have been suspended until further notice," the website said.
"Customers holding tickets with final destination to Kabul will not be accepted for travel at their point of origin.
"Affected customers should contact their booking agents or the local Emirates office for rebooking options."