In recent days, City Hall saw the governor as unfair in tarnishing Mr. de Blasio’s support of organized labor, while Mr. Cuomo’s circle grumbled that the mayor’s legislative lobbying was more about his efforts to burnish his national profile.

And behind the scenes, there were other matters at stake, centered in part around Mr. de Blasio’s hiring of Karen Hinton as his new press secretary.

The spat began days after word leaked of the hiring of Ms. Hinton, an experienced public relations hand who has known both men since working with them in the 1990s at the Department of Housing and Urban Development. She is also married to Howard Glaser, a onetime senior aide to Mr. Cuomo.

The governor, who prizes loyalty, was surprised by the appointment, and irritated that a person he had considered part of his inner circle was headed to work for a rival, according to several people briefed on the matter who were granted anonymity to describe private and sensitive conversations.

These people said the governor was upset that his office did not hear about the appointment first from either the mayor, Ms. Hinton, or Mr. Glaser.