May stops just short of endorsing Murray in a blog post on the Green party's website.
She praises Murray for advancing the idea of Liberals, New Democrats and Greens joining forces in the next election to ensure defeat of Prime Minister Stephen Harper's Conservatives — an idea May herself has long championed.
Saying she won't endorse any Liberal leadership contender, May adds it's "pretty obvious" that a good showing by Murray would advance their shared interest in electoral co-operation.
She notes that some Greens signed up as New Democrats in last year's NDP leadership race in order to support Nathan Cullen, who advanced a similar plan for electoral co-operation among so-called progressive parties.
May says Greens are now asking her advice on whether to get involved in the Liberal race; she doesn't explicitly try to dissuade them.
"All I can say is that we need our supporters to remain active in the Green party," she says in the blog post.
"Nevertheless, it is pretty obvious that Joyce Murray doing well in the leadership race should advance the shared goals and objectives held by Greens, by NDPers who supported Nathan and by many across a political, progressive spectrum," May adds.
"In that spirit, I want to publicly salute Joyce Murray for charting a difficult course, displaying political courage and integrity. Let’s hope the goals of co-operation and electoral reform gain ground through her efforts."
Under Murray's proposal, local riding associations would be empowered to hold run-off nominations to choose a single progressive candidate to square off against the Tories in vulnerable ridings.
She says it would be a one-time measure aimed at defeating Harper in the next election. After that, she would reform the electoral system so that each party's share of the seats in the House of Commons better reflects their share of the popular vote.
NDP Leader Tom Mulcair has flatly rejected any sort of peace pact with the Liberals or Greens.
Murray continues to hope he'll change his mind if public pressure for co-operation builds. But she has said co-operation would still work if just the Liberals and Greens joined forces.
However, May was surprisingly cool to that idea in a recent interview.
She said she's become gun shy about doing any kind of deal with just one party after her experience in the 2008 election, when she agreed to a "courtesy" non-compete pact with then-Liberal leader Stephane Dion. Each party agreed not to run a candidate against the other party's leader.
"We got so slammed by the NDP and it was so vicious that I'm afraid to do anything like that for fear of having people say the Greens are somehow associated with the Liberals," May said.
"I can't see allowing the Greens to be seen as some kind of affiliate of another party."
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