Suffolk Conservatives are backing Republican Randy Altschuler in his bid to unseat incumbent Democrat Rep. Tim Bishop, but Cox has been trying to force a Conservative Party primary via petition. The GOP has remained neutral in the Cox-Altschuler contest.
"Christopher, you should withdraw your candidacy and support Randy Altschuler," Walsh said in a letter written to Cox on Tuesday and released Wednesday.
"Our shared responsibility for taking back this seat must be about the mission and not the individual; it's the right thing to do for Suffolk County and for America," the letter said.
Cox later released a long letter to Walsh laying out the rationale for his campaign and arguing that while it was important to have a single candidate on both the Republican and Conservative lines, "you'll agree having the right candidate is more important."
The Walsh letter came as the Cox campaign was dealing with reports that it was losing some campaign operatives. The campaign responded with a statement saying it was changing its focus from the first phase of "listening to the priorities of Suffolk County voters," and was moving on "to harness the overwhelming grassroots support we have already developed."
Cox is the grandson of former President Richard Nixon and the son of state GOP chairman Edward Cox.