New York’s subway has long been the lifeblood of the city, but delays have increased and a series of accidents have raised concerns over safety. As the century-old system grapples with aging infrastructure and a booming ridership of nearly six million people each day, New Yorkers have grown increasingly frustrated that they cannot rely on the subway to get them where they need to be in a timely manner.

It was not the first time the authority has tried to take on the problem of subway delays — officials released a six-point plan in May focused on the Eighth Avenue line in Manhattan. But the combination of Mr. Lhota’s credibility and the growing urgency over the near-constant problems has raised the stakes.

Mr. Lhota, who ran against Mr. de Blasio for mayor in 2013, returned to lead the authority in June to help turn around the subway after an earlier stint as chairman. Asked on Tuesday whether the agency might raise fares if the city did not provide funding for the rescue plan, Mr. Lhota dismissed the idea.

The authority would continue to stick to its schedule of modest fare increases every two years, Mr. Lhota told reporters. “Raising fares is not an option,” he said.

Last month, Mr. Cuomo, a Democrat who might be considering a presidential run in 2020, declared a state of emergency for the subway and tasked Mr. Lhota with submitting a rescue plan within 30 days. But after Mr. Cuomo appeared to take responsibility for the crisis, the governor argued last week that the city owned the subway system and should take a primary role in fixing it.

On Tuesday, the authority assembled an advisory board to assist with the rescue plan, including former Mayor David N. Dinkins, a mentor and ally of Mr. de Blasio who sat in the front row at the news conference. In a statement, Mr. Dinkins said he saw how critical the subway was to the city during his time as mayor and urged elected leaders to work together.

Throughout the day, aides to the mayor and the governor had spent time calling interest groups and potential allies to argue their case in the dispute between Mr. de Blasio and Mr. Cuomo, according to three people with direct knowledge of the calls who were not authorized to discuss them publicly. The lobbying effort provided another example of how City Hall and Albany are jockeying for political advantage, both in front of the cameras and behind the scenes, on an issue that could be potentially damaging to both leaders.