Green Party Leader Elizabeth May says she will not stay on as leader of her party for another four years but intends to run again and continue to serve as a Member of Parliament for the B.C. riding of Saanich-Gulf Islands.

"I don't think I will stay on as leader for four more years. I will run again, I hope. As long as my health holds up I'd love to be the Member of Parliament for Saanich-Gulf Islands for another term and I'd love to work with another leader," May said during a news conference at her constituency office Thursday.

"For the near term I think it's very important for the health of the party that I continue as leader."

May said that her future as leader is not a decision that she will take alone. She said she wants to consult with the other two Green MPs who were elected on Monday, Paul Manley, in Nanaimo-Ladysmith, and Jenica Atwin, in Fredericton, first.

May said that in a minority government an election could happen sooner rather than later, complicating her transition out of the leadership, but that it is her intention to leave her role atop the party.

"I think the chances are very slight that I would be leading the Green Party into an election in 2023, if the next election is spring of 2020 I think it's more likely I would be leading the Green Party into that election," she said.

Open letter to Trudeau

May opened the news conference saying that she had written to Prime Minister Justin Trudeau to lay out areas of common policy between them, where she thinks she can work with the Liberal minority government — goals such as bringing in a single-use plastic ban and adopting more civil behaviour in the House of Commons.

In the letter, released Thursday, May calls climate change action the "single most important" issue facing the new House of Commons. She called on him to create an internal panel with all party leaders to make sure climate measures are "collaborative and well-informed by science."

She urged Trudeau to "ratchet up" Canada's emission reduction targets in advance of the Santiago Climate Change Conference in December.

"To improve humanity's chances of survival, it is critical that Canada assume a leadership role, first ramping up our own ambition and then pushing for more ambition overall in global negotiations," May wrote in her letter to Trudeau, which she also sent to the other party leaders.

May said Canada's emissions target can be changed by cabinet without Parliament's approval.

The Green Party finished with three seats in Monday's election. The party gained one seat, but remains in fifth spot.

How the 338-seat House of Commons breaks down, by party, after the 2019 election. (CBC News)

The Liberals won 157 seats, which is 13 shy of a majority. That means they will need the support of other parties to pass legislation and budgets. It also means the Greens don't hold the balance of power.

Still, that didn't stop May from reminding Trudeau that she would not back up his government unless it set more ambitious climate targets.

"We cannot vote confidence at any point, on a confidence motion, in a government that fails to have a climate target that's grounded in science and consistent with what the intergovernmental panel on climate change says we must do," she said Thursday.

May noted in her letter that the Liberal, NDP and Green election platforms all promised to bring in pharmacare, and suggested the parties could collaborate to expedite the introduction of a national program.

"Can we (Liberal, NDP and Green) agree to make it universal and effective, as recommended by the Hoskins Report? Can we commit to making it a priority to be accomplished in 2020?" she wrote.

May also said there is broad consensus among the parties to:

Improve mental health care.

Address the opioid crisis.

Support seniors.

Increase affordable housing.

Reduce cell phone charges.

Protect elections from domestically sourced "untruths."

May also proposed striking a committee on murdered and missing Indigenous women and girls, with the goal of adopting the recommendations in the final report of the national inquiry.

While she acknowledged it's a more "difficult" issue, May also is pressing for electoral reform — despite Trudeau's broken promise to change the current process. May says Canada needs to move to proportional representation, and has suggested a ranked ballot system such as a single transferable vote as an alternative to the existing "first-past-the-post" system.

She also called for all leaders to respect the rules of the House and to "not heckle or act disrespectfully" toward the Speaker or other members.

"Greens believe it is important that we try to compromise where compromise is possible and work together so that the 43rd Parliament can be as productive as the Liberal minority of former Prime Minister Lester B. Pearson," reads the letter to Trudeau.