With speculation growing that Mr Livingstone's candidature would be blocked before the vote in two weeks time, the former health secretary said in a newspaper interview: "It would be better if he ran from everybody's point of view."
Mr Dobson also criticised the leadership's decision to abandon one member, one vote in favour of an electoral college including MPs and unions, and said that this could damage him.
Mr Dobson was bullish about his prospects in the race to become the Labour candidate and attacked the former Greater London Council leader for wanting to become mayor in order to act as "leader of the opposition" to the Prime Minister.
"I want to win this contest on goals scored - not on complaints about the ref," Mr Dobson said. "He should run and after that there can be no more excuses."
The comments will make the already politically sensitive task of barring Mr Livingstone from standing even more difficult for Downing Street.
It is widely believed that the Labour leadership has been considering ways in which to influence the vetting panel against Mr Livingstone.
Mr Dobson is keen to avoid the impression that the election has been "stitched up" in his favour. Downing Street's support for Alun Michael's candidature in the race to be First Minister for Wales became a poisoned chalice when local party members felt that influence from the capital had become an imposition.Reuse content