"We don't know what to do now," said one young woman, sitting next to a pile of suitcases and plastic bags outside the heavily guarded front gate of the international terminal.
The unclear legal status for South Sudanese in the north is one of many unresolved issues between the former foes since the South gained independence in July under a peace agreement.
Khartoum has ruled out dual citizenship for more than 500,000 southerners who have lived in the north for decades and started treating of them as foreigners on Monday after the end of a grace period.
Until Sunday flights to the southern capital Juba had been conducted at the domestic terminal without passport controls.
But many are now stuck in limbo, since South Sudan has failed to open an embassy in Khartoum that can issue passports.
At the airport, hundreds of South Sudanese tried checking into their flights to Juba early on Monday but immigration officials denied them entry.
"They need passports to board flights," a Sudanese police officer said inside the terminal.
Both presidents were meant to sign agreements last week to allow citizens free residency but Sudan's President Omar Hassan al-Bashir called off a summit with his southern counterpart Salva Kiir after border fighting broke out.
With almost no passengers to check in, state-owned Sudan Airways and other local carriers suspended their Juba flights.
"We are ready to fly but wait for a political decision," said an official at Sudan Airways. The Sudanese foreign ministry could not be reached for comment.
Around 500 South Sudanese queued outside the embassy building but were unable to get passports or temporary travel documents since it is not yet fully functional. Khartoum has ruled out dual citizenship.