Brown delivered his speech just as word circulated that he would not seek the 2020 Democratic presidential nomination.
Murphy, one-time law clerk to former U.S. Supreme Court Justice Anthony Kennedy, served as state solicitor under Gov. Mike DeWine when DeWine was Ohio attorney general for six years.
He argued cases involving appeals before the Ohio Supreme Court, the 6th Circuit and the U.S. Supreme Court.
But Murphy provoked fierce opposition from Brown when he filed papers in 2015 with the U.S. Supreme Court arguing that Ohio’s ban on same-sex marriage did not violate the U.S. Constitution. The justices that same year found Ohio’s law unconstitutional, by a 5-4 vote.
President Donald Trump last year nominated Murphy and Chad Readler, who was confirmed Wednesday, to replace Alice Batchelder and Deborah Cook, who are taking senior status.