US Democratic presidential candidate Hillary Clinton announced her victory in the Kentucky primary while her opponent Senator Bernie Sanders won in Oregon, the BBC reports.
Mrs Clinton remains the front-runner to secure the nomination in July, with a significant delegate lead.
But Mr Sanders again resisted pressure to drop out of the race, saying he was "in until the last ballot is cast".
Mrs Clinton only narrowly won Kentucky. With most of the votes counted she was less than 0.5% ahead.
But Alison Lundergan Grimes, chairwoman of the Kentucky State Board of Elections, told CNN that unofficial results confirmed that Clinton would narrowly win the state's primary contest.
Shortly afterwards, Mrs 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 Tuesday 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 Mr Sanders, a senator from Vermont who has historically been an independent, not a Democrat, to drop out of the race.
But he said he still has a path to the Democratic nomination.
Speaking at the California rally, Mr Sanders recognised his campaign's "steep hill to climb" but called for his supporters to remain hopeful and "take our fight into the convention" in July.
But senior party figures are pressing the Vermont senator 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 Mr Sanders faced a "test of leadership".
And Democratic National Committee chairwoman Debbie Wasserman Schultz described Mr Sanders' response to the violence as "anything but acceptable".