The Government spent £6 million in the first four months this year on hand-outs to asylum seekers who agreed to go home.
Immigration Minister Liam Byrne said 1,956 took part in the pilot scheme, which was expanded in January from a project which offered no cash but £1,000 in assistance grants.
The more generous handout led to a 108 per cent leap in numbers taking part, compared with 943 in the first four months of last year.
As a result the pilot will be extended for another six months, Mr Byrne said.
The Voluntary Assisted Return and Reintegration Programme is open to failed asylum seekers and those who withdraw outstanding applications.
Only those who applied for asylum before January 1 this year can apply for the enhanced package, and they must leave the UK between July 1 and the end of the year.