Gordon Brown is not ruling out a change in the law on organ donation even though a panel of experts has rejected the idea of “presumed consent”.
The UK Organ Donation Taskforce said assuming organs could be used unless people opted out was unlikely to boost donation rates.
A £4.5m public awareness campaign in England will be aimed at boosting voluntary donor numbers.
But the prime minister warned if it did not work a law change may follow.
The UK has one of the lowest organ donation rates in Europe.
There are currently around 8,000 people in the UK who need an organ transplant but only 3,000 operations are carried out each year.
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Every year, 1,000 people in the UK die after waiting for a transplant.
Currently, people must sign up to the organ donor register – or their families must agree – before their organs can be used.
Health Secretary Alan Johnson announced on Monday that £4.5m would be spent on a public education campaign aimed at signing up 20 million people to the organ donor register by 2010, and 25 million by 2013.