The pool of potential candidates vying for U.S. Representative Lee Zeldin’s seat in 2018 just shrank, as State Assemblyman Fred W. Thiele Jr. of Sag Harbor said this week that he will not, in fact, run.

“I’ve been leaning that way for a while,” Mr. Thiele said on Monday.

Mr. Thiele had been considering a run against the Republican congressman since at least mid-July, when he traveled to Washington, D.C., to meet with members of the Democratic Congressional Campaign Committee, despite his membership in the Independence Party.

After that meeting, Mr. Thiele expressed doubts about his ability to be effective as a member of an especially discordant and divisive Congress.

His doubts remained the determining factor in his decision. “In my position, with my experience and contacts, I have the power that comes with that position—much more than I would have as a 65-year-old freshman in Washington,” he said.

He added that October 1 means the launching of another fundraising period for congressional candidates, and that he felt compelled to clear the way for those who are definitely running, or still deciding, to allow them to beef up their war chests.

According to the Zeldin for Congress Federal Election Commission records, after two quarters of fundraising, the incumbent has $762,249.93 cash on hand for the 2018 general election.

Mr. Thiele’s decision is especially significant for Suffolk County Legislator Kate Browning of Mastic, a friend and respected colleague of Mr. Thiele’s; both previously expressed reluctance to run if the other did. Ms. Browning said on Monday that she was still making up her mind but plans to announce her intentions next week.

Ms. Browning is term limited and finishes out her sixth and final term on the County Legislature in Hauppauge at the end of the year, meaning she is unable to run again for her current seat this November. She also switched her registration from the Working Families Party to the Democratic Party in May, though the change will not take effect until after the election.

“I have a great working relationship with Kate Browning and I have the highest respect for her,” Mr. Thiele said. “She would make a great candidate,” he added, saying that he won’t make a formal endorsement until the field of candidates is fully formed.

So far, the confirmed Democrat candidates looking to challenge Mr. Zeldin next year include: Vivian Viloria-Fisher, a former Suffolk County legislator from East Setauket; Perry Gershon of East Hampton, a chief investment officer at Jefferies LoanCore LLC; Elaine DiMasi, a physicist at Brookhaven National Laboratory who lives in Ronkonkoma; and Brendon Henry, a bartender from Center Moriches.