The former secretary of state remains the front-runner in the Democratic race to secure the nomination in July, with a significant delegate lead.
However, Bernie Sanders again resisted pressure to drop out of the race, saying he was “in until the last ballot is cast”.
Hilalry Clinton only narrowly won Kentucky. With most of the votes counted she was less than 0.5% ahead.
Alison Lundergan Grimes, chairwoman of the Kentucky State Board of Elections, told CNN that unofficial results confirmed that Hillary Clinton would narrowly win the state’s primary contest.
Shortly afterwards, Hillary Clinton tweeted: “We just won Kentucky! Thanks to everyone who turned out. We’re always stronger united.”
In the Republican race, Donald Trump won the party’s only contest on May 17 in Oregon, which was no surprise as he was the only candidate left in the race.
The Kentucky Democratic primary will award 60 delegates to go to the party’s convention in Philadelphia while Oregon’s primary will award 74.
Pressure is rising on Bernie Sanders, a senator from Vermont who has historically been an independent, not a Democrat, to drop out of the race.
However, he said he still has a path to the Democratic nomination.
Speaking at the California rally, Bernie Sanders recognized his campaign’s “steep hill to climb” but called for his supporters to remain hopeful and “take our fight into the convention” in July.
Senior party figures are pressing Bernie Sanders to do more to bring his supporters into line, after some of them disrupted a state convention in Nevada last weekend.
Majority leader Harry Reid said the Vermont senator faced a “test of leadership”.
Democratic National Committee chairwoman Debbie Wasserman Schultz described Bernie Sanders’ response to the violence as “anything but acceptable”.
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