But auctioning tax credits would require legislative approval. Mr. Murphy said on Friday that he had “already begun those conversations.”

Stephen M. Sweeney, the Senate president, did not return requests for comment.

The two men have had a checkered legislative record since Mr. Murphy became governor in January. Working together, they passed some progressive bills on issues like voting rights, immigration and the environment, but they disagreed bitterly over the so-called millionaire’s tax, leading to a fight that nearly shut down the government.

Still, Mr. Murphy said he is “pretty optimistic, actually” that he will have the needed legislative support.

Will the fund compete with major venture capital firms?

No. New Jersey is looking to partner with the firms.

The state does not want to be solely responsible for vetting pitches and business plans. Instead, it would partner with a venture capital firm once that firm had decided to invest.

If, for example, an entrepreneur is seeking $20 million to launch a product and finds a venture capital firm willing to invest, the firm can then request that the state split the cost. The goal, according to the governor’s office, is to minimize the private company’s risk while offering an incentive to provide funding to start-ups in New Jersey.

Mr. Murphy said he has not spoken to any venture capital firms yet.

Chris Sugden, a managing partner at Edison Partners, a New Jersey-based venture capital firm, said he liked the idea.

“ Having the New Jersey program come in to put 50 percent of the bucks to match it, that’s pretty attractive,” Mr. Sugden said.