As Bettel spoke, a small but noisy crowd, many of whom were British nationals living in Luxembourg, clapped and cheered.
Meanwhile, crowds were already gathering outside Luxembourg's government buildings, where the meeting with Bettel was scheduled. The British government source said officials requested an indoor location for the post-meeting media briefing in order to avoid the chants of protesters.
The decision to go ahead with the press conference against the wishes of British officials was a pointed move on the part of Bettel. Typically, host nations go to great lengths to avoid humiliating allies in this way.
Brexit was not the choice of the EU but that of the UK's Conservative government, Bettel said. "You can't hold our future hostage for party political gains," he said, adding: "I repeat this Brexit is not my choice."
Speaking to UK media away from the protestors, Johnson gave his reasons for canceling the press conference. "I don't think it would've been fair to the prime minister of Luxembourg," he said. "I think there were clearly going to be a lot of noise and I think our points might've been drowned out."
Johnson admitted Brexit negotiations would have to be accelerated, and that the EU must make "movement" over the Irish backstop but added that there was "just the right amount of time" to do a deal.
But the British proposals remain unclear and Juncker said the EU was still waiting to hear of a workable alternative to the backstop.
In a statement after the talks, Juncker said the aim of the meeting was to "take stock" of the ongoing Brexit negotiations and to discuss the "next steps."
The Commission President said it was "the UK's responsibility to come forward with legally operational solutions that are compatible with the Withdrawal Agreement," adding that "such proposals have not yet been made."
"The Commission will remain available to work 24/7," Juncker's statement continued. "The EU27 remain united."
Downing Street said Johnson had used the meeting to repeat his assertion that he will not request an extension to the October 31 deadline for Britain's departure from the European Union.
"The leaders agreed that the discussions needed to intensify and that meetings would soon take place on a daily basis," Johnson's spokesperson said.
"It was agreed that talks should also take place at a political level between Michel Barnier and the Brexit Secretary, and conversations would also continue between President Juncker and the Prime Minister," the PM's spokesperson added.
A UK government source said that despite the bad headlines from the abandoned press conference, the day had been constructive. "If you ignore the noise, let's look at what happened during the PM's visit. He had a good meeting with Jean Claude-Juncker where they agreed to intensify talks. We need to start accelerating talks if we're going to make further progress."
"This is on the back of positive meeting in Dublin last week. If EU are prepared to move on the backstop -- rejected three times by Parliament -- then we can see the rough shape of a deal. We are working in a positive and determined way to get a new deal."
The Downing Street statement added that Johnson "reconfirmed his commitment" to the 1998 Good Friday agreement, which helped bring about peace in Northern Ireland after decades of sectarian violence, and that he still had a "determination to reach a deal with the backstop removed."
Aimee Lewis wrote from London. Matthew Chance reported from London and Nina dos Santos reported from Luxembourg.