Families should overcome the "fatal reluctance" to talk aboutorgan donation, the Health Secretary urged as he launched a consultation into plans for an opt-out system.
Jeremy Hunt said people need to have an open conversation and make their wishes clear to relatives in order to save the lives of patients waiting for a transplant.
Prime Minister Theresa May announced in October that the Government will shift towards an organ donation system in England which presumes consent.
Mr Hunt said: "Every day three people die for want of a transplant, which is why our historic plans to transform the way organ donation works are so important.
"We want as many people as possible to have their say as we shape the new opt-out process.
"But as well as changing the law, we also need to change the conversation - it can be a difficult subject to broach, but overcoming this fatal reluctance to talk openly about our wishes is key to saving many more lives in the future."
Around 6,500 people are currently waiting for a transplant in the UK, but in the past year 1,100 families decided not to allow organ donation because they were unsure or did not know whether their relatives would have wanted to donate, according to NHS Blood and Transplant.
While 80% of people say they would be willing to donate their organs, only 36% are officially registered and just half of adults on the register have discussed their wishes with a family member, the Department for Health said.
The consultation, launched on Tuesday, will examine issues including how much say a family should have over a person's decision to donate their organs, how different groups will be affected by the new system and when exemptions to "opt-out" might be needed.
Millie Banerjee, chairwoman of NHS Blood and Transplant, said: "We support any initiative which leads to more organ donors and more lives being saved.
"We hope the consultation starts a national conversation about organ donation. If you want to donate, please tell your family now."
Simon Gillespie, chief executive of the British Heart Foundation, said: "Introducing an opt-out system in England will mean more people get the life-saving heart transplant they desperately need.
"In the meantime, it's still important for all of us to have conversations with our loved ones about organ donation so our wishes can be met if the worst should happen."
The consultation, which is available online, will close on March 6.