Voters in Ireland rejected two proposed changes to the country’s Constitution that would have removed language about women’s duties being in the home and broadened the definition of family beyond marriage, dealing a blow to the government that analysts said suggested the weakness of their campaign to pass the proposals.

While the decisions will have no practical implications for the law, the results, announced on Saturday, saw the proposals defeated by a wide majority, an unexpected defeat for equality campaigners and for the coalition government of Leo Varadkar, the taoiseach, or prime minister.

Despite support for a vote in favor of both proposals from all major political parties, some critics had said the proposed clauses didn’t go far enough, while others criticized what they saw as phrasing that was too broad.

Mr. Varadkar, speaking Saturday after most votes had been counted, said it was clear that the proposals had been defeated.

“As head of government and on behalf of the government, we accept responsibility for the result,” he said. “It was our responsibility to convince the majority of people to vote ‘Yes,’ and we clearly failed to do so.”

Irish citizens had gone to the polls on Friday to vote in two referendums to amend the country’s 87-year-old Constitution, which was drafted at a time when the Roman Catholic Church’s influence on many aspects of life in Ireland was immense.