South Jersey businessman and political power broker George E. Norcross III is willing to cooperate with an investigation into state tax incentives — but not the one that Gov. Phil Murphy commissioned earlier this year, according to a lawsuit filed Tuesday by Norcross and several companies against the governor and members of a special task force.

The five-count suit, filed in Mercer County, claims the task force was formed unlawfully and wants it disbanded. It is the latest escalation in tensions between Norcross and the governor — both Democrats — since a public hearing May 2, when investigators questioned the veracity of claims in tax credit applications submitted by Norcross’ insurance brokerage and organizations tied to him.

The companies are “extremely interested in cooperating" with an inquiry by the legislature, Norcross attorney Kevin Marino said on a conference call with reporters. But when it comes to the governor-appointed task force, he said, “we’re dealing with an investigation that goes well beyond what the statute permits.”

Other lawyers on the call spoke more bluntly. “This is our response: We’re bringing it on,” said Michael Critchley, a reference to a recent interview given by task force special counsel Jim Walden, a New York-based attorney who is named in the suit.

The tax credit applications submitted by the companies are “in full compliance” with regulations, the suit says. The Economic Development Authority (EDA) is not a department in the executive branch, the suit contends, and falls outside of the governor’s investigative powers.

Norcross’ legal team also continued to invoke an argument that the task force has unfairly “singled out” Camden, where the EDA has directed corporate tax breaks worth $1.6 billion. Companies with links to Norcross and his brother Philip, an attorney, won approvals for $1.1 billion in tax credits, an investigation by ProPublica and WNYC found.

Any effort to halt progress and revitalization efforts in Camden “has consequences,” said Norcross attorney William Tambussi, adding, “This is the wrong place to settle a political score.”

A spokesperson for the governor said the administration would “vigorously” defend the investigation in court. “The task force is about ensuring that the tax incentive programs are operated to the benefit of everyone in New Jersey, not just a select, connected few,” Darryl Isherwood said in a statement.

In its response, the task force reiterated that it had already invited the companies to bring forth witnesses at an upcoming hearing.

“Rather than responding to that offer, they have filed an unfounded lawsuit against the task force instead,” the task force said in a statement. "The public can judge this tactic for what it is.”

Murphy created the task force by executive order in January after the state comptroller found “significant” problems with EDA oversight of $11 billion in tax credit programs, including the agency’s ability to verify whether companies created promised jobs.

So far, task force investigators have focused on allegations that companies lied to obtain credits, and they have uncovered evidence of how tax credit legislation was influenced behind the scenes.

Plaintiffs in the suit include the insurance brokerage headed by Norcross, Conner Strong & Buckelew, along with NFI, the Michaels Organization, and Cooper University Health Care, which Norcross chairs. Collectively, the firms won approval for $285 million in tax credits.

The law firm Parker McCay, where Philip Norcross is managing shareholder, is also a plaintiff. A Parker McCay attorney made changes to the draft tax credit legislation that benefited clients, according to a report by the New York Times.

Parker McCay has said it complied with laws on lobbying and offered “input” on the bill to help Camden — one of the poorest cities in the state — at the request of legislators.

A barrage of calls and meetings between Parker McCay and EDA officials was the subject of another report by ProPublica and WNYC, published just minutes before the lawsuit was announced Tuesday. The firm sought bigger tax breaks and expedited reviews for clients, the report said, citing thousands of pages of internal documents.

Staff writer Andrew Seidman contributed to this article.