"Neither party — neither the EU nor London — is actually content with the fact that talks have not exactly gone at the originally hoped for pace," Kaljulaid said following the meeting according to an Office of the President press release. "But it is important to remain within the framework agreed upon at the beginning of negotiations, which means that first we will discuss the details of the U.K.'s exit and only thereafter can we begin discussing what the cooperation model will be like following Brexit."

The Estonian president stressed that the 27 remaining member states of the EU are united on this issue.

According to Kaljulaid, the pressure of time can be increasingly felt with each passing day, and in order to remain on schedule, it is necessary to reach agreements regarding the details of Brexit over the next week.

"I hope that the [two] sides will reach an agreement regarding citizens' rights and finncial agreements as well as the matter of the border between Ireland and Northern Ireland during Estonia's presidency of the Council of the EU," Kaljulaid said, adding that there were clear time constraints ahead of December's European Council that could affect this.