They each won several states in primary elections on Tuesday to propel them over the finish line.

The two 2020 contenders will provide the US with its first rematch in a presidential election for 70 years.

Polling suggests it will be a tight race that will come down to narrow margins in a few key states.

The nominations will be made official at party conventions this summer.

The 81-year-old president said on Tuesday evening that he was "honoured" voters had backed his re-election bid "in a moment when the threat Trump poses is greater than ever".

Citing positive economic trends, he asserted the US was "in the middle of a comeback", but faced challenges to its future as a democracy, as well as from those seeking to pass abortion restrictions and cut social programmes.

"I believe that the American people will choose to keep us moving into the future," Mr Biden said in a statement from his campaign.

Incumbency gave Mr Biden a natural advantage and he faced no serious challengers for the Democratic nomination.

Despite persistent concerns from voters that his age limits his ability to perform the duties of the presidency, the party apparatus rallied around him.

Meanwhile, Mr Trump, 77, remains very popular with the Republican voter base, which has propelled him to victory in primary after primary over well-funded rivals.

His campaign for a second term in the White House has zeroed in on stricter immigration laws, including a pledge to "seal the border" and implement "record-setting" deportations.

Mr Trump has also vowed to fight crime, boost domestic energy production, tax foreign imports, end the war in Ukraine and resume an "America first" approach to global affairs.

Tuesday night's results do not come as a shock, as both men have dominated their races so far.

Both their re-nominations seemed all but predetermined, despite polling that indicates Americans are dissatisfied with the prospect of another showdown between Mr Biden and Mr Trump in November.

The US presidential primaries and caucuses are a state-by-state competition to secure the most party delegates.