Nassau Republicans and Democrats announced a new cross-endorsement agreement for state Supreme Court justices Tuesday, building on a pact inaugurated last year and now will last into the 2016 presidential year.

Under the deal, both major parties in November will back two judicial candidates chosen by Republicans and two picked by Democrats.

The pact largely is an outgrowth of a dispute between Nassau GOP chairman Joseph Mondello and Suffolk Conservative Party chairman Edward Walsh. In the past, Walsh used his committee's dominating vote in the Conservatives' bicounty judicial conventions to pressure the GOP for more nominations.

Originally, Democrats were slated this year to get cross-endorsements for two of their candidates to one for Republicans. The political calculus changed when Republican Appellate Justice Peter Skelos, brother of state Sen. Dean Skelos (R-Rockville Centre), unexpectedly retired earlier this year, creating a new vacancy that was not part of the original deal.

In return, both sides agreed to extend the deal to next year, although details of those future cross-endorsements are not yet settled because it is unclear how many judgeships will be involved.

Democrats' Supreme Court candidates will be Robert McDonald, the county party's former first vice chair who stepped down Monday, and County Court Judge James McCormack, an acting Supreme Court justice since 2006.

McDonald is a veteran criminal defense lawyer who recruited Democrat Kathleen Rice, now a congresswoman, to run her first race for Nassau district attorney. McCormack will get the nod because he stepped aside last year when the major parties made their first cross-endorsement agreement.

Republicans will name Family Court Judge Julianne Capetola and Jack Libert, a former Oyster Bay public works and planning commissioner who also served as town zoning board of appeals chairman. Capetola is the stepmother of Michele Johnson, an Oyster Bay Town Board member.

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Republicans and Democrats will hold their bicounty Supreme Court nominating conventions Thursday night.

Mondello ended a three-decade-long ban on major party cross endorsements after Walsh in 2012 used hardball tactics to get an extra conservative judicial nominee. The two had a lengthy telephone shouting match that held up the GOP convention for hours and resulted in Mondello punching a locker and breaking a finger.

Mondello in 2013 made a cross-endorsement deal with Suffolk Democratic chairman Richard Schaffer that cost Walsh an extra nomination he had sought as well as one already promised. Last year, Mondello made his first cross-endorsement pact with Jacobs.

Suffolk Republicans, Democrats and Conservatives have yet to formally name their candidates for three other Supreme Court openings. Republican incumbent Emily Pines is seeking re-election, and two other seats are open because Justice Patrick Leis has reached the mandatory retirement age of 70 and state Administrative Judge A. Gail Prudenti resigned last month.