The significant intervention by the former chair of the liberal One Nation caucus of Conservative MPs came after the Tory Reform Group on the left of the party refused to endorse either right-wing candidate.
This was followed by Tory moderates announcing they would boycott a contest where the last centrist candidate James Cleverly was eliminated by MPs, meaning there was only a choice of two members from the right of the party.
Mr Green described these reports as "disturbing" and warned that liberal Tories like him still need to choose the best candidate to rebuild the party, and one who will give them a voice in that process.
Speaking exclusively to The Independent, Mr Green said: "Since the final two candidates for the Conservative leadership have been chosen there have been disturbing reports of moderate party members saying they won't vote. They supported one of the other candidates and they now feel neglected.
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