Edgars Rinkēvičs said there was a “very considerable risk” that, with time rapidly running out, Britain could crash out of the bloc without a withdrawal agreement.
He will meet Mr Hunt, the foreign secretary, in Riga today, with the Brexit high on the agenda.
Mr Hunt’s visit is part a three-day trip that will also take in Denmark and the Netherlands. It forms part of a concerted effort by UK ministers to convince their European counterparts to support Theresa May’s Chequers plan, which has already been dismissed by the EU’s chief negotiator, Michel Barnier.
The Independent‘s petition to give the public a Final Say on Britain’s future relationship with the EU has now been signed by more than 600,000 people.
Asked about the prospects of a Brexit deal, Mr Rinkēvičs told the BBC Today programme: “We are at a very critical point.
“I believe that both the EU and UK need to have extra effort to reach some kind of deal by October because I believe it is in the best interests of both the EU and UK.
He added: “I think it is only now the British public and British government understand how complex, how difficult, this kind of Brexit is and that it is very difficult to build the future relationship.”
Assessing the likelihood of an agreement being reached, he said: “Frankly at this point I would rate it 50:50. 50:50 is a very considerable risk.”
He also suggested UK attempts to win European leaders’ support for the Chequers proposals despite opposition from the European Commission would not work.
He said: “From our point of view the EU is united as 27 [countries]. We are also satisfied to see that there is a more detail position of the British government that constitutes a good ground for really trying hard to reach a deal. So having said 50:50, I would say I am remaining optimistic.”
Mr Rinkēvičs said he had “full confidence” that Mr Barnier “is doing his best”, and that the EU 27 would not “split our position” and start bilateral talks with the UK.
Theresa May has repeatedly insisted a Brexit deal based on the Chequers plan is achievable, but Liam Fox, the international trade secretary, has said there is only a 40 per cent chance of an agreement.
Asked about the chances of a no-deal Brexit, he told the Sunday Times last week: “I have never thought it was much more than 50-50, certainly not much more than 60-40”.
He said the EU was concerned about the prospects of Britain crashing out without an agreement, and that this was crucial to securing a good deal for Britain.
He said. “I think it’s essential that ‘no deal’ looks credible to the EU. If it’s causing some anxiety in Britain — think what it’s causing in Brussels.
“If our message on ‘no deal’ is becoming more credible and resonating with those we are negotiating with in Europe, then our negotiating hand is getting stronger every day and we shouldn’t do anything to undermine that.”
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.