Billionaire businessman Donald Trump and Democrat Bernie Sanders have won their parties' presidential primary contests in Oregon, as Hillary Clinton claimed victory in a neck-and-neck battle in Kentucky.

The Democratic primary race in Kentucky was too close to call, but Mrs Clinton declared on her Twitter feed: "We just won Kentucky! Thanks to everyone who turned out. We're always stronger united."

With almost all the votes counted, the former US secretary of state held a narrow lead of less than one-half of 1 percent as she tried to avoid ending the primary season with a string of losses to Vermont senator Mr Sanders.

Mr Trump won the sole Republican contest in Oregon and socialist Mr Sanders was declared the Democratic winner shortly after the polls closed in the liberal-leaning state.

Rallying supporters in Carson, California, Mr Sanders said he would end up with about half of the delegates in Kentucky and promised to press forward even though he would need to win about two thirds of the remaining pledged delegates to overtake Mrs Clinton.

"Before we will have the opportunity to defeat Donald Trump, we're going to have to defeat Secretary Clinton," he said.

Mrs Clinton holds a commanding lead of nearly 300 pledged delegates over Mr Sanders and a dominant advantage among party officials and elected leaders known as superdelegates.

Nearing the end of a long primary slog, the two Democratic candidates are preparing for June 7 primaries in California, New Jersey and four other states and then the District of Columbia primary on June 14.

When pledged delegates and superdelegates are combined, Mrs Clinton is now about 96% of the way towards securing the Democratic nomination.