The report by the Organ Donation Taskforce Group said an opt-out or 'presumed consent' system may not increase donation rates and might cause significant complications.
Johnson announced an organ donation awareness campaign designed to boost the donor register to 20 million people by 2010 and 25 million people by 2013, the Department of Health said in a news release.
"If, however, we do not see the number of organ donations rising and progress is not being made we will revisit the issue of whether a change in the law is needed," Johnson said in a statement.
Only 25 percent of the population is currently on the United Kingdom's organ donor register, the Department of Health said.
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