UNITED NATIONS—Yemen’s warring political factions were on the verge of a power-sharing deal when Saudi-led airstrikes began a month ago, derailing the negotiations, the United Nations envoy who mediated the talks said.

Jamal Benomar, who spearheaded the negotiations until he resigned last week, told The Wall Street Journal the Saudi bombing campaign against Iran-linked Houthi rebels has hardened positions on a key point—the composition of an executive body to lead Yemen’s stalled transition. This will complicate new attempts...