Mr Morgan, the MP for Cardiff West, has sent a detailed list of complaints to Unity Security Balloting Services (USBS), which was appointed to oversee the contest.
The controversy, which follows three months of bitter campaigning, is also set to be raised at the next meeting of Labour's ruling national executive committee (NEC).
Mr Morgan, who was beaten on Saturday by Alun Michael, the Welsh Secretary, in the battle to become First Secretary of the Welsh Assembly, said that he had serious concerns about the ballot of 21,000 party members.
In a letter passed to The Independent, the backbencher demanded to know why ballot papers had been sent out three days early without his knowledge, allowing his opponents a crucial head-start in the race.Letters from MPs supporting the Welsh Secretary had mysteriously gone out at the same time, he said. Even Anita Gale, general secretary of the Wales Labour Party, had not been informed by Millbank of the change of date.
Mr Morgan also demanded to know if USBS had opened ballot envelopes to give Millbank and his opponents an indication of the results. When the final results were announced, the backbencher won the vote among party members by 65 per cent to Mr Michael's 35 per cent. Mr Morgan demanded to know how his opponents were able to make an accurate prediction a week earlier, apparently discounting the possibility of it being an informed guess. He claimed there was a prima facie case that information had been leaked, perhaps by an individual rather than by USBS.
USBS is one of three semi-charitable institutions used for ballots. A party political ballot does not require the organisers to meet statutory standards or controls. USBS refused to comment and referred all inquiries to Labour's press office.
A party spokesman said there had been no leaks and the party had total confidence in USBS. "It's pretty pathetic. Rhodri was big enough to accept the result on Saturday," he said. He denied that any ballot papers were opened before the poll had closed. They were sent out early because the printers had finished them early.
However, the use of the union block vote to clinch the contest for Mr Michael has angered many in the Wales party. Mr Michael narrowly won the contest by gaining more support among trade unions and assembly candidates in Labour's electoral college.
Mr Morgan said last night:"If they can't produce a categorical written assurance that there was no leak to Millbank and to the Alun Michael camp, then it is a deeply unsatisfactory situation."