Mr. Trump said his victory in the 2020 election was critical to preventing the country from being hijacked by the “radical left,” which he said was “consumed by rage and radicalism and insatiable lust.” And he said that House Democrats had begun impeachment proceedings because “they know they can’t beat us fairly.”

Mr. Trump’s advisers earlier in the day previewed the new executive order as part of Mr. Trump’s commitment to protecting Medicare. Seniors “like what they have, so the president is going to protect it,” Alex M. Azar II, the secretary of health and human services, said in a conference call with reporters. Mr. Azar also used the call to frame Democrats’ health care plan as too focused on reducing the ranks of the uninsured.

The executive order seeks to beef up Medicare Advantage, the plans offered by private insurers that contract with Medicare and currently cover about a third of the program’s 60 million beneficiaries, according to senior administration officials. The order also calls for lowering Medicare Advantage’s premiums, allowing providers to spend more time with patients and reducing Medicare fraud.

The executive order, originally called “Protecting Medicare From Socialist Destruction,” was renamed “Protecting and Improving Medicare for Our Nation’s Seniors” before Mr. Trump’s speech. But administration officials said the renaming was a distinction without a difference.

Joe Grogan, the director of the White House Domestic Policy Council, said the goal was still to contrast the administration’s commitment to protecting seniors with “the vision for Medicare as a one-size-fits-all, single-payer system” supported by many Democratic candidates.

“Medicare for all is Medicare for none,” added Seema Verma, the administrator of the Centers for Medicare and Medicaid Services, who has been a vocal critic not just of the Democratic proposals but also of the Affordable Care Act. “Proposals like Medicare for all, as well as the public option, they are morally wrong because they would demote American seniors to second-class status.”

Democrats competing for their party’s presidential nomination strongly disagree: All advocate expanding health care coverage, though their strategies to do so vary.