In a letter dated Thursday, a lawyer for Ben & Jerry's said the companies wanted to "attempt to resolve their dispute through expedited formal mediation" instead of litigating and would use "best efforts" to finish within two weeks.
The letter was filed just 20 minutes before a scheduled hearing on the matter in Manhattan federal court.
Lawyers for Ben & Jerry's and Unilever did not immediately respond to requests for comment.
Ben & Jerry's opposes selling its products in the West Bank, saying it would undermine its brand and the "social integrity" built since Ben Cohen and Jerry Greenfield founded the company in a renovated Vermont gas station in 1978.
It sued on July 5 to block the sale of the Israeli business to the licensee Avi Zinger, saying Unilever had guaranteed Ben & Jerry's the right to protect its brand when buying the company in 2000.
Unilever countered that it was "fully empowered" to conduct the sale, which could not be undone because it has already closed.
It also said Ben & Jerry's could not show irreparable harm, and that prolonging the impasse risked exposing both companies to further "intense public criticism."
Most countries consider Israeli settlements in the West Bank illegal.
Ben & Jerry's decision last July to end sales there and its ties with Zinger prompted some Jewish groups to accuse the company of anti-Semitism, and some investors to divest their Unilever stock.
Unilever has more than 400 brands including Dove soap, Hellmann's mayonnaise, Knorr soup and Vaseline skin lotion.