Those not registered anywhere in Turkey face life in refugee camps, with some Syrians saying people have already been rounded up by police in Istanbul and deported back to Syria.
About 500,000 Syrians are registered in Turkey’s largest city but a similar number are thought to live there without proper papers.
Human Rights Watch has accused the authorities of detaining and coercing Syrians into signing “voluntary return forms” then deporting them to danger.
Interior Minister Suleyman Soylu said on Tuesday during an interview with Turkish TV channel Haberturk that the deadline had been extended and that refugees could relocate and register in any other province apart from Antalya, a popular holiday destination in the south of the country, which is also not admitting Syrian refugees.
Students and their families, as well as those with officially registered jobs in Istanbul, would be exempted from the need to relocate.
Turkey hosts more than 3.6 million Syrians, the largest population of Syrians displaced by an eight-year civil war.
Mr Soylu said that about 347,000 Syrians had returned to their country so far.
A series of truces brokered between Turkey and Russia has failed to end fighting in the northwestern Idlib province, where Ankara has a dozen military positions.
Anecdotal reports say Syrians have been forced across the border into Idlib province, where the Syrian military launched an offensive against the final rebel stronghold in late April, forcing almost half a million people to flee to safer areas further north.
On Tuesday, the main insurgent group in the province pulled out of a critical rebel town as government forces advanced in the area amid intense bombardment and air strikes. Earlier in the week, a Turkish military convoy reportedly on its way to the town was hit by Syrian air strikes.