For the second time this week, Mayor Bloomberg has publicly attacked Governor Pataki — this time over one of his vetoes.

Mr. Bloomberg issued a statement yesterday afternoon criticizing the governor for vetoing a bill that would have given the city’s police commissioner, Raymond Kelly, a permanent seat on the board of the Port Authority of New York and New Jersey.

“Even though the NYPD is the most sophisticated counterterrorism police force in the world, much of New York City’s transportation infrastructure is policed by the MTA and the Port Authority,” Mr. Bloomberg said.

“I am particularly disappoint in the Governor’s veto because between the time this bill passed both houses of the Legislature and the time the Governor vetoed it last night, another Al Qaeda was planning to flood Ground Zero and Lower Manhattan by attacking Port Authority facilities,” the mayor added, referring to a terrorist threat earlier this summer to bomb a PATH tunnel or the retaining walls that block out the Hudson River.

The clash between the mayor and governor is particularly noteworthy because it is the second one this week.

On Monday, Mr. Bloomberg criticized the governor for signing legislation that would force the city to increase payments and benefits to emergency responders who became ill from their work in the World Trade Center recovery effort after September 11, 2001. Mr. Bloomberg said that while he is not opposed to the intent of the law, that the city can’t afford it and Albany should be the one paying.

He also suggested that it was unfair to provide greater benefits to police and fire officials who were killed on September 11 than to those killed in the line of duty on other days.

A spokeswoman for Mr. Pataki, Joanna Rose, defended the governor’s veto decision and said, “A mandatory appointment is not what is needed to keep New Yorkers safe from Al Qaeda.”

In his veto message, Mr. Pataki said the city already has four of the 12 commissioners on the board and that its interests are adequately represented.

“Approval of this bill would establish a precedent that other municipalities could cite in seeking representation on the Port Authority,” he said.

Still, the relationship between Messrs. Bloomberg and Pataki seems to be souring as the governor’s time in office winds down. At the very least, Mr. Bloomberg has been more willing to take him on in recent days.

A spokesman for the mayor, Stuart Loeser, downplayed the clash for a second time this week, saying, “The mayor does what he thinks is best for the city and the governor does what he thinks is best for the state.”

The latest bill would have increased the number of commissioners on the board to 14 from 12, with Mr. Kelly and a New Jersey police official as the two new members. Some suggested that Mr. Pataki might have been pressured by rival police forces to reject the bill. Others said concerns last year voiced by Mr. Kelly over security at the proposed Freedom Tower delayed construction and angered Mr. Pataki. Ms. Rose denied that.

Mr. Bloomberg declared his intent in January in his State of the City address to push for this legislation that would give Mr. Kelly a permanent seat on the boards of both the MTA and the Port Authority. In 2003, he appointed his then budget director to the MTA board.

Assemblyman Michael Cusick, a Democrat of Staten Island who sponsored one of the bills at Mr. Bloomberg’s request, said he also was disappointed and understood the mayor’s ire.