After a brief hiatus last week, the Bloomberg ad about pre-existing conditions was back on the air Friday through Monday. Mr. Bloomberg is now running another ad that notes that more people are uninsured under Mr. Trump than under President Obama.

A spokeswoman for Mr. Trump’s campaign defended the president’s record, claiming he “has protected Americans with pre-existing conditions by offering affordable health care with choice and patient-guided decision-making.” She also pointed to steps he’s taken to give people “access to short-term, limited duration plans and association health plans.”

But under the law, these cheaper plans are not required to cover pre-existing conditions. And Mr. Trump has for years sought the repeal of the Affordable Care Act, which includes a rule that people cannot be denied coverage or charged higher premiums because of their health status; both practices used to be widespread.

The second half of Mr. Bloomberg’s ad broadly touches on his own health care platform, announced in December. He proposes creating a so-called public option — an insurance plan that would be run by the government, and that people could buy with the health insurance subsidies that the Affordable Care Act currently provides.

The advertising blitz underscores the unorthodox nature of Mr. Bloomberg’s presidential campaign. He is not participating in the primary debates or churning through five event days on the campaign trail, and is skipping the first four nominating states. He has shown no desire to spar with his Democratic rivals on health care, and is instead focusing his vast personal wealth on targeting the president. His strategy has helped him rise in some national polls, but has not translated into a move into the top tier.

Polling by his campaign found that health care costs are the top financial concern for families, and that a general sense of insecurity about health coverage is causing many voters to want to cling to the system they have.

With the Iowa caucuses less than a week away, some voters are voicing that anxiety.

Nathan Mundy, a lawyer from Des Moines, cited health care as a top concern as he waited for former Vice President Joseph R. Biden Jr. to speak at a campaign event in Indianola, Iowa, on Saturday.