At a Shriver news conference, Duran said some in the gay and lesbian community had expressed disappointment that he -- an openly gay man and civil rights lawyer -- did not back first-place finisher Sheila Kuehl, an LGBT pioneer in California's Legislature.
Duran responded that Shriver's views were closer to his more conservative business philosophy and that he didn't want to give his endorsement based on race, gender or sexual identity.
"Those who demand equality have to extend equality," Duran said.
Shriver and Sheila Kuehl will face each other in the Nov. 4 general election. Both actively courted Duran, who received 16% of the vote in a field of eight candidates.
Shriver, a member of the Kennedy political clan and a former Santa Monica council member, finished seven percentage points behind Kuehl, who received 36% of the vote.
Shriver said he had gotten to know Duran during the primary campaign as someone who was "passionate about getting problems solved." He also noted that he and Duran had served in local government, as opposed to Sacramento.
Shriver said he and Duran agree that L.A. and other cities' efforts to boost the economy should not wait for solutions to "come down magically from Sacramento." All of Kuehl's experience is as a state lawmaker.
In a separate interview with The Times, Kuehl said that although she would have preferred to get Duran's endorsement, she doesn't see it as affecting her chances of winning in November. An analysis of primary voter turnout shows that she carried some 75% of voting precincts, including West Hollywood, which Duran has represented for 14 years.
Kuehl noted that since the primary she's been endorsed by Los Angeles Controller Ron Galperin, City Atty.
Last month Duran said he would back the candidate who is primarily concerned with the county's fiscal health. "They are both a little more liberal than I am,'' he said after the June primary. "So I'm still concerned about who's going to hold the solid center of the county."