Boris Johnson has said it does not really matter which lobby group is chosen to "carry the flag" for EU exit in the up referendum campaign.
The Electoral Commission will decide whether to select Vote Leave, which Mr Johnson is backing or Grassroots Out, which has been endorsed by UKIP's Nigel Farage, as the official lead campaign.
The winner will be able to spend up to £7m on TV broadcasts and advertising.
The Mayor of London suggested the two groups would unite after the decision.
Relations between the two groups have been strained amid arguments over campaign strategies and personalities.
Asked whether a merger was now on the cards, he told LBC Radio that the "basic objective" should be to have a single campaign and the rival groups were "unified by the rightness of their arguments".
Vote Leave has been endorsed by Mr Johnson and the five Conservative Cabinet ministers who want to leave the EU. It also has the backing of a number of Labour Eurosceptics, including Gisela Stuart, and business figures.
Grassroots Out, which was formed in January, is backed by senior UKIP figures as well as Conservative and Labour backbenchers such as Peter Bone and Kate Hoey.
Speaking on his monthly LBC phone-in, Mr Johnson rejected suggestions that having two separate groups was holding back the Leave campaign and was being exploited by their opponents.
"I haven't noticed the other side making very much of this. Let's hold our fire and not get wrapped up in tiny issues about who is doing what on the Leave campaign. The thing that matters to me is getting the arguments out."
Mr Johnson said he had spoken to the UKIP leader in recent weeks but his focus was on making the case to the British people.
He added: "The Electoral Commission have to work out which of the various groupings should carry the flag for Britain to take back control of its borders, take back control of a huge amount of money and forge new trading relationships around the world.
"I think it doesn't really matters too much who comes out on top in this one provided that we all get together and work to that end."
Asked whether the decision would be a unifying moment for those backing EU exit, he replied "of course it will".
The elections watchdog is expected to make its decision on which group will head the Leave campaign by the middle of April. It will judge each applicant's merits on the basis of a range of criteria, such as level of cross-party support, campaign tactics and organisational capacity.
Whoever wins will get access to a grant of up to £600,000 and an overall spending limit of £7m for media, mailshots and campaign organisation.
Conservative MP Tom Pursglove, one of the co-founders of Grassroots Out, said the designation would be a "watershed moment", after which all Leave campaigners should "put aside their differences, row in together and campaign as one".
He said he expected there to be dialogue between the two groups in the run-up to the official decision and Boris Johnson was "spot on" to argue the issue could not be allowed to become a distraction.
"There is just not the time to waste on bickering over the designation. We should be focused purely on leaving and winning this referendum."
During the phone-in, Mr Johnson likened the Remain campaign's warnings about the risks of EU exit to fatalistic predictions about the Millennium Bug in 2000, saying talk of "bank accounts being wiped" and "planes falling out of sky" back then had been proved to be groundless.
But he was challenged by the Labour MP Chuka Umunna, who accused him of using the campaign for his own political ends and "inviting a media circus" to his house last month to announce he was backing EU exit.
"What you need to understand is that this is not about you," Mr Umunna, who backs EU membership, said. "It is about our city and our country...If anybody has been talking down our country, it is you. You denigrate our influence within the EU."
Mr Johnson said that what made people sceptical about the EU was listening to politicians such as Mr Umunna "droning on" about the economic benefits of EU membership. "This is about the prospects of the British people and their democracy," he insisted.