Former President Donald J. Trump held a Fourth of July-themed rally on Saturday night in Sarasota, Fla., across the state from where a tragedy has been unfolding for more than a week as firefighters, search dogs and emergency crews search for survivors in the collapse of a residential building just north of Miami Beach.

The political rally in the midst of a disaster that has horrified the nation became a topic of discussion among aides to the former president and Gov. Ron DeSantis of Florida, a Trump ally whose growing popularity with the former president’s supporters is becoming an increasing source of tension for both men, according to people familiar with their thinking.

After officials from the governor’s office surveyed the scene of the condominium collapse in Surfside, Fla., Adrian Lukis, chief of staff to the governor, called Michael Glassner, a longtime Trump aide who is overseeing the Florida event, according to people familiar with the discussion. In a brief conversation, Mr. Lukis inquired whether the former president planned to continue with the event given the scale of the tragedy, two people said.

He was told there were no plans to reschedule.