An outbreak of Legionnaires’ disease in the South Bronx appeared to be ebbing on Friday, even as city and state officials jockeyed to show how they were responding to the airborne illness.

The New York City health commissioner, Dr. Mary T. Bassett, said there had been no new fatalities and only one new case reported in the last day, in what has become the worst outbreak of Legionnaires’ disease in the city’s history. A total of 101 people have been sickened since July — 10 of whom have died.

Since the city learned of the outbreak in late July, health officials investigated the area, eventually narrowing in on five water-cooling towers in the South Bronx that were found to have the legionella bacteria. On Thursday, city health officials issued an order requiring buildings with the towers to inspect and clean them within two weeks.

That, apparently, was not sufficient for the state. On Friday, state health officials convened a meeting and news conference with investigators from the federal Centers for Disease Control and Prevention, at the Manhattan office of Gov. Andrew M. Cuomo.