WASHINGTON—Green Party presidential candidate Jill Stein is aggressively courting disaffected supporters of Vermont Sen. Bernie Sanders, potentially undermining Democratic efforts to unify the party behind presumptive nominee Hillary Clinton.

Ms. Stein, the presumptive Green Party nominee, has been making the case in interviews, rallies and appearances across the country that supporters of Mr. Sanders should consider casting a ballot for her in the fall, emphasizing the common agenda and progressive worldview they share.

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