Major news organizations have become increasingly wary of sending journalists to travel with President Trump to White House events and campaign rallies, as the president and his aides continue to shun safety protocols after an outbreak of the virus within their ranks.

The New York Times, The Wall Street Journal and The Washington Post are among the major outlets that have declined to assign reporters to travel with Mr. Trump as he returns to the trail this week, saying they do not have assurance that basic precautions will be taken to protect reporters’ health.

Foremost among the flouters is Mr. Trump himself, who, despite recently contracting the virus and spending three nights in the hospital, has shown little willingness to change his habits: On Saturday, he said the virus would soon “disappear,” and on the way to a rally in Florida on Monday, he boarded Air Force One — where reporters were seated in the cabin — without wearing a mask.

At least three White House correspondents have tested positive for the coronavirus in the past two weeks, including a Times reporter who had traveled on Air Force One, Michael D. Shear.

Safety concerns may also complicate Mr. Trump’s tentative NBC town hall on Thursday. NBC executives have asked the White House for proof that their employees will not face undue risks at the event, according to two people familiar with discussions.