Senior diplomats say special consideration should be given to those who are desperate to return home but do not have the funds to pay for the fares.
They say the budgets of embassies are limited and if large numbers of people choose to leave the country, it would be impossible for them to foot the bill.
The amnesty, which began last Wednesday, will run until December 31.
It aims to help thousands of people who came into the country on visit visas and stayed after their documents expired or whose sponsors failed to renew their papers.
It will allow illegal immigrants to legalise their stay or leave the country without penalty.
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