By Steve Holland

MANCHESTER, New Hampshire (Reuters) -U.S. President Joe Biden won an unusual Democratic write-in vote in New Hampshire's primary election on Tuesday, an important display of political strength, despite his name not being on the ballot.

Edison Research projected Biden the winner over two Democrats whose names were actually on the ballot - U.S. Representative Dean Phillips of Minnesota and self-help author Marianne Williamson.

The victory for the incumbent president was the end product of a fervent write-in campaign orchestrated by New Hampshire Democrats, who were troubled by the national party's decision to send the state's first-in-the-nation primary election to more diverse South Carolina.

At an watch party by organizers of the write-in campaign, some in the audience booed when the speakers noted that New Hampshire's proud tradition of vetting Democratic candidates had been ended by the Democratic National Committee.

But the crowd cheered when it appeared Biden was going to do well.

"Based on the preliminary numbers we're seeing, it looks like it's going to be really, really big victory and a great night for Joe Biden," said Donna Soucy, state Senate Democratic leader and a write-in campaign advocate.

Biden had 73% of the vote with 31% of the write-in counted, while Phillips had about 20%.

The 55-year Democrat had said in the days leading up to Election Day that he would continue his campaign. He has argued that Biden is weak and unelectable and vulnerable to defeat by the likely Republican nominee, Donald Trump.

Biden supported the move by national Democrats to move their first primary election to South Carolina.

Whether his victory will be seen as sufficiently strong will probably be debated by his rivals.

A CNN/University of New Hampshire poll released on Sunday showed Biden drawing 63% of the primary vote in that state, with Phillips at 10%.

Democratic supporters had sought to temper expectations. They point to the 39% support that Senator Lisa Murkowski won during a write-in election in 2010 as a sign of what Biden might achieve.

Phillips had made some inroads with New Hampshire voters.

Margaret Flynn of Nashua, New Hampshire, said she voted for Biden in 2020 but expects to vote for Phillips.

"I think Biden's too old to be president, I think he's kind of outdated, and I'm not sure he can beat Trump," she said after a Phillips event in Nashua.

The White House has repeatedly dismissed concerns about 81-year-old Biden's age, though polls show voters are concerned about it.

Biden wins write-in vote in New Hampshire