Failed Republican senate candidate Roy Moore is still refusing to concede the Alabama senate election despite US President Donald Trump calling on him to admit defeat.

Mr Moore has sent a fundraising email to supporters asking for contributions to his “election integrity fund’ so he could investigate reports of voter fraud.

“I also wanted to let you know that this battle is NOT OVER!” he wrote.

The former judge was defeated by Democrat Doug Jones by about 20,000 votes earlier this week. It is the first time a Democrat has held the seat since 1992.

Under Alabama law, a recount is only triggered if a winning candidate’s lead is less than 0.5 per cent.

But Mr Moore, whose campaign dogged by allegations of sexual misconduct with teenage girls during the 1970s, is yet to concede the race to fill the seat previously held by US Attorney General Jeff Sessions.

He told supporters the vote was “close” and some military and provisional ballots were not expected to be counted until next week.

Mr Moore said his campaign was collecting “numerous reported cases of voter fraud” to send to the secretary of state’s office.

Secretary of State John Merrill has nonetheless said it is unlikely last-minute ballots will change the outcome of the election or even trigger a recount.

He added his office had investigated claims of voting irregularities but “had not discovered any that have been proven factual in nature.”

Alabama Senate race: Roy Moore vs Doug Jones Show all 12 1 /12 Alabama Senate race: Roy Moore vs Doug Jones Alabama Senate race: Roy Moore vs Doug Jones Democratic senatorial candidate Doug Jones speaks to reporters after voting Getty Images Alabama Senate race: Roy Moore vs Doug Jones Republican Senatorial candidate Roy Moore (L) and his wife Kayla ride their horses to the polling station to vote AFP/Getty Images Alabama Senate race: Roy Moore vs Doug Jones David Watson waves in a Santa suit as he holds a Doug Jones sign AP Alabama Senate race: Roy Moore vs Doug Jones Republican Senatorial candidate Roy Moore speaks to the media as his wife Kayla (R) looks on AFP/Getty Images Alabama Senate race: Roy Moore vs Doug Jones Democratic Alabama Senate candidate Doug Jones casts his vote at Brookwood Baptist Church REUTERS Alabama Senate race: Roy Moore vs Doug Jones Roy Moore speaks to the media after he rode in on a horse to vote AP Alabama Senate race: Roy Moore vs Doug Jones Democratic candidate Doug Jones greets supporters after casting his ballot AP Alabama Senate race: Roy Moore vs Doug Jones Republican Senate candidate Roy Moore departs on horseback after he cast his ballot in Gallant REUTERS Alabama Senate race: Roy Moore vs Doug Jones Voters wait in line to cast their ballot at a polling station setup in the St Thomas Episcopal Church Getty Images Alabama Senate race: Roy Moore vs Doug Jones Democratic Senatorial candidate Doug Jones (L) greets voters outside of a polling station at the Bessemer Civic Center Getty Images Alabama Senate race: Roy Moore vs Doug Jones Voters exit after casting their ballots at a polling station setup in the Fire Department Getty Images Alabama Senate race: Roy Moore vs Doug Jones Democratic Alabama U.S. Senate candidate Doug Jones speaks with the media after casting his vote at Brookwood Baptist Church Reuters

Mr Trump, who had endorsed the Republican candidate, called Mr Jones to congratulate him on his victory and said on Friday said that he believed Mr Moore should concede.

The Alabama Republican Party has also urged its supporters to accept the result, which has seen the state elect its first Democratic senator since 1992.

The final results of the race are expected to be certified between December 26 and January 3 after counties report official totals.