UK and EU leaders have said new momentum is needed in negotiations on their future relationship, after high-level talks on Monday.
The PM, who met EU Commission President Ursula von der Leyen virtually, said there was a "very good" chance of getting a trade deal by December.
He said he saw no reason why it cannot be "done in July", after the sides agreed to intensify talks next month.
Mrs von der Leyen said they "agreed to deliver the best deal" for citizens.
The EU also noted the UK's decision not to extend the transition period, which ends in December.
In a joint statement issued after Monday's meeting via video conference, the UK and EU "welcomed the constructive discussions on the future relationship that had taken place".
"The parties agreed nevertheless that new momentum was required," it said.
They have agreed to intensify talks in July, and to find an "early understanding on the principles" underlying any deal.
The UK government has said the talks in July will involve a mix of formal negotiating rounds and smaller group meetings in London and Brussels, if coronavirus guidelines allow.
'Tiger in the tank'
Mr Johnson said the EU and the UK were "not that far apart" with regards to the future relationship, but he added that "a bit of oomph" was needed in the talks.
Calling on the EU to "put a tiger in the tank", the prime minister said the chances of getting a trade deal by the end of the year were "very good", provided both sides focus now and "get on and do it".
Asked what the cut-off date would be by which the UK government will give business certainty of what they can expect, Mr Johnson said he saw no reason why it cannot be "done in July".
"I certainly don't want to see it going on until the Autumn/Winter as I think perhaps in Brussels they would like. I don't see any point in that so let's get it done."
European Council President Charles Michel, who joined Mrs von der Leyen on the call along with European Parliament President David-Maria Sassoli, said a "broad and ambitious agreement" was "in our mutual interest".
Interesting choice of words by President of European Council following videoconference with Boris Johnson👇Translation: EU wants a good deal with U.K. but not at any price .. #brexit https://t.co/fiZb0AuMcB— katya adler (@BBCkatyaadler) June 15, 2020
And Mr Sassoli tweeted in Latin that "agreements must be kept".
Important EU-UK meeting with @vonderleyen @eucopresident and @BorisJohnson. The European Parliament wants an ambitious and comprehensive agreement, in line with the joint commitments made in January. Pacta sunt servanda.— David Sassoli (@EP_President) June 15, 2020
Joint statement → https://t.co/L1JYUVdx37 pic.twitter.com/lTLaYYfK5B
Downing Street earlier said Mr Johnson would reiterate that the UK's ambition is for a high quality free trade agreement consistent with others the EU have agreed.
Mr Johnson was also due to make clear that the UK is ready to start trading on World Trade Organisation rules from 1 January if a deal cannot be reached.
This was Boris Johnson's first meeting with EU leaders since trade negotiations started back in March.
So, did we have an "aha moment"? A glimpse of light at the end of the tunnel of deadlocked talks?
Well, not exactly. But this was always going to be a stocktaking moment, rather than high level negotiation.
The EU was buoyed to hear the prime minister express commitment to finding a deal.
And while Brussels privately regards as unrealistic, the UK aim of having the outline of that deal in place by the end of the summer, EU insiders say negotiators will try everything to find agreement as soon as possible.
You wouldn't expect them to say anything less.
But notably absent from today's declarations was to what extent each side is willing to compromise.
And that, of course, will be key.
Without some concessions, from both sides, today's high-level declaration of intent to reach an EU-UK deal, is rather empty.
But a French former Europe minister has said the EU is preparing itself for a no-deal Brexit.
MEP Nathalie Loiseau told BBC Radio 4's Today programme: "We are ready either for an agreement or for a no-deal and we are getting prepared more actively to a no-deal considering the circumstances.
"We believe it is possible to have an agreement - it has to be ready in October so that parliaments on both sides can ratify it.
"We believe it is possible because we have the political declaration which we negotiated together, signed together and should respect together - so, yes, the framework is here."
Monday's virtual meeting comes after EU chief negotiator Michel Barnier said there had been "no significant areas of progress" at the last negotiating round earlier this month.
Likewise his UK counterpart David Frost had said progress "remains limited," and negotiators were "reaching the limits" of what could be achieved in formal talks.
Differences between the two sides remain on fisheries, competition rules, police co-operation, and how a deal would be enforced.
Meanwhile, Downing Street confirmed that Mr Johnson and Emmanuel Macron will meet in London on Thursday.
The French president will travel to London to attend official commemorations of 80th anniversary of General Charles de Gaulle's appeal to the French population to resist the German occupation of France during the Second World War.