Mr Sanders’ plan would expand Medicare, the government programme which covers the elderly, to everyone.
His “Medicare for All” bill would mean Americans no longer having to pay out-of-pocket charges when visiting doctors and hospitals.
Instead, they would get health coverage by showing a new government-issued card.
The bill omitted specifics about how much the scheme would cost.
Aides to Mr Sanders said it would be funded by people paying monthly premiums to the government instead of to insurance companies.
Those premiums would range from zero for the poorest to high levies on the rich and corporations.
President Barack Obama’s “Obamacare” programme helped more than 20 million people, who previously could not afford it, to obtain health insurance.
Mr Trump wants to repeal and replace Obamacare saying it represented overreach by the government and is “imploding”.
Some 28 million Americans are still uninsured and would be covered by Mr Sanders’ plan.
Katie Martin, a spokeswoman for Senate Republicans, said: “We welcome the Democrats’ strategy of moving even further to the left.”