“Who are you to decide what the legislative priorities are for loyal Democrats across New York State?” Mr. Felder wrote, urging Mr. Klein to “unify with your Democrat colleagues and not just highlight a handful of issues that attempt to distinguish you from the Republican conference.”

Mr. Felder’s letter may further complicate the perplexing political calculus in the Senate, which has been the scene of high drama in the last decade and simmering tension during the tenure of Gov. Andrew M. Cuomo, who took office in 2011, the year that Mr. Klein and the Independent Democratic Conference split from the main group of Democrats in Albany.

Since then, the conference has helped Republicans rule, entering into a power-sharing agreement in 2012 and often garnering perks like larger offices and staffs. The partnership has continued even though there have sometimes technically been more Democrats in the Senate, if Mr. Felder and the conference members are counted.

With the election on Tuesday of Brian Benjamin to fill a vacant seat in Harlem, Democrats again hold a numerical majority, 32 to 31. But the mainline Democrats hold only 23 seats, after subtracting the eight Independent Democratic Conference members and Mr. Felder.

On Monday, Mr. Klein’s group began a campaign, Call the Roll, that asked Democrats to sign a pledge to uphold seven “key progressive issues,” including ones that have not been embraced by their Republican colleagues, like the expansion of abortion rights, public campaign finance and single-payer health care. The campaign was christened with a three-and-a-half-minute promotional video and a letter to all Democrats, including Mr. Felder, who Mr. Klein has previously said was responsible for tipping the balance of power in the Senate.