Boris Johnson warned that getting a Brexit deal would "not be easy" and people should not "hold their breath" awaiting a breakthrough.
Speaking to reporters in Devon today he said the "mood music" on his visits to Germany and France was "very good".
"They could see that we want a deal, they can see the problems with the backstop. Clearly Angela Merkel thinks that the solutions can be found within 30 days - actually what she meant was if you can do it in two years you can certainly do it in 30 days.
"But I want to caution everybody, OK? Because this is not going to be a cinch, this is not going to be easy. We will have to work very hard to get this thing done."
The Prime Minister added: "We have to have an arrangement that allows the whole UK to come out of the EU and have frictionless trade at the border in Northern Ireland.
"There are lots of ways that we can make sure that happens.
"But to persuade our EU friends and partners, who are very, very, very hard over against it, will take some time.
"I'm afraid we will have to prepare to come out without an agreement and we can do that, we are very confident that we will be OK because we will have all sorts of preparations in place."
He added: "We are making progress but I am just telling people not to hold their breath, because I have seen the way these Brussels negotiations work."
It was "always on the steps of the court, as it were, that the deal is done", he said, and "I must urge people - we are going to be working very hard on this but they shouldn't necessarily get their hopes up too soon".
Meanwhile, the UK Government is determined British cities and communities will receive "similar" funding if EU cash is withdrawn after Brexit, the Northern Powerhouse Minister has said.
Jake Berry said British versions of structural funds from the EU would help the UK flourish and there would be new trading opportunities after Brexit.
Speaking in Liverpool on BBC Radio 4's World at One programme, Mr Berry said there is a "chink of light" in negotiations with the EU.
He said the Government still hopes to get a deal despite "tooling up" its departments for the prospect of a no-deal.
Asked whether he could promise money from the EU will be replaced by the Government, Mr Berry said: "First of all, it is important to note it is not the EU's money, of course.
"It's our money that they are top-slicing and then sending some of it back in Liverpool.
"I lived in Liverpool in the 1990s, I know the huge difference it made to this city having Objective 1 status.
"I am determined that this UK-shared prosperity fund, a British version of those structural funds, will support great cities and communities across the north of England in a similar way."