Sen. Bernie Sanders's (I-Vt.) campaign on Thursday hit back at President Trump, a day after the White House attacked Sanders's "Medicare for all" bill.

"This campaign's message to Trump is simple: we welcome this fight because we are going to defeat you in the election and guarantee health care as a right to all people," Sanders campaign manager Faiz Shakir said in a statement.

The back-and-forth highlights the role that health care could play in the 2020 election, with Republicans thinking that attacking Medicare for all is a winning strategy, but Sanders welcoming the fight after a number of Democrats focused on the health care issue while winning control of the House in 2018.

Several other Democratic White House hopefuls have backed Sanders's bill, including Sens. Kamala Harris (D-Calif.), Cory Booker (D-N.J.) and Elizabeth Warren (D-Mass.), though some of them have also touted more incremental solutions.

Republicans have zeroed in on Sanders's plan eliminating private health coverage and replacing it with a government plan.

"Self-proclaimed socialist Senator Bernie Sanders is proposing a total government takeover of healthcare that would actually hurt seniors, eliminate private health insurance for 180 million Americans, and cripple our economy and future generations with unprecedented debt," the White House said on Wednesday, in response to Sanders introducing his updated bill.

Shakir pointed to Trump's previous praise of single-payer health care before he became president.

"Donald Trump, who used to express his admiration for single-payer health care, has decided to put out statements that do the bidding of the largest insurance and pharmaceutical companies," Shakir said. "Trump is defending industries of greed that throw millions of Americans off their health coverage while paying health industry CEOs more than $1 billion in a single year."

Separately, Democrats have also attacked Trump for backing a lawsuit seeking to overturn ObamaCare.

Trump has countered that he wants to come up with a better plan than the Affordable Care Act, but has not offered any specifics while stating that Republicans will be the "party of health care."