Estonian Prime Minister Juri Ratas was unable to make the Rīga rendezvous, leaving Estonian ambassador to Latvia Arti Hilpus to fill in alongside Kariņš and Lithuanian Prime Minister Saulius Skvernelis.
The three said that despite reports in the British press that the UK government intended to plead its case for re-opening the so called "Brexit negotiations" via the Baltic states, no such approaches had been made. They also signaled that any such attempt would likely be fruitless.
"It took two years to reach the agreement on the Brexit deal. It was a tough negotiation... It's not realistic to get agreement from 27 countries within three weeks on a deal which was shaped over a period of two years," said Kariņš.
"'The UK faces an immense challenge. Over a long period of time they have not decided exactly what kind of deal they would like to have but from the Latvian perspective the withdrawal of the UK is a very unfortunate fact. The UK is a very important strategic partner but we must take care of the European Union and its unity."
"We agreed among the Baltic countries that it is very important that Europe remains united," he said.
"If there is a better agreement possible on the backstop with regard to the Northern Ireland border, it would be welcome, but I am very sceptical because this has been two years in the making... there is a solution that has been tabled and everyone [in the EU] is okay with the solution," said Kariņš.
Lithuania's Prime Minister Skvernelis adopted a similar tone, pointing out that his country had a large diaspora population in the UK but that European unity remains paramount.
"Negotiations have been completed and now the initiative is on the side of the UK. This hard work that has been done over the last two years cannot be changed by a last-minute proposal."
"Now the ball is in the court of the UK," Skvernelis said, "but I do not see any opportunity for restarting negotiations which were started from zero. Now we have to implement the agreement that has already been achieved."