Murphy, 46, and Edmonds, 40, traded vows on New Year's Day on a private island off Bora Bora in French Polynesia in a ceremony that was not legally binding.
"While the recent symbolic union in Bora Bora was representative of our deep love, friendship and respect that we have for one another on a spiritual level, we have decided to remain friends," the statement said.
The statement did not clarify whether the two remained a couple. In an e-mail exchange, Robinson said he could not comment beyond the statement.
Murphy has six children from previous relationships. He and Edmonds, whose credits include "Dreamgirls" and "Beverly Hills Cop," began dating last year. They became engaged in July.