Malaysia has warned illegal migrant workers they have until the end of January to leave the country or face fines, whipping and jail sentences.
An amnesty allowing an estimated one million, mostly Indonesian, migrants to leave without penalty was extended in the wake of the tsunami.
No decision has yet been taken on whether to expel refugees from Aceh.
The deadline for economic migrants to leave has been extended twice already, both times at the request of Jakarta.
But though Indonesia's resources are still stretched coping with the devastation in Aceh, Malaysia has signalled that it will wait no longer.
'Harassed by authorities'
According to the government's news agency, Deputy Prime Minister Najib Tun Razak says an estimated 1.2 million illegal migrants have been given quite enough time to leave already.
Jakarta will soon have to decide how to deal with hundreds of thousands of returnees.
Malaysia's home minister has described the presence of so many undocumented foreigners as a national emergency.
They are widely blamed for rising crime levels, and the government says it will mobilise up to 500,000 armed reservists and community volunteers to detain them.
The fate of around 30,000 Acehnese who fled the fighting between separatists and the Indonesian army however has yet to be decided.
Mr Najib said the government will study their situation.
Before the earthquake and tsunami, the United Nations refugee agency, the UNHCR, had already registered more than 10,000 people from the province.
However the Malaysian government has not signed international treaties on refugees and many who have sought sanctuary here say they are regularly harassed by the authorities.
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