The meeting took place as part of a working visit of President Kaljulaid to Moscow, where she participated in the opening of the newly renovated Estonian embassy.

The two presidents met for a short meeting in a smaller circle, followed by a working lunch that included officials from both sides. While some Russian government members were present, no Estonian ministers accompanied President Kaljulaid on her trip.

According to a Thursday evening press release of the Office of the President, the two heads of state discussed bilateral relations, economic cooperation and the broader international situation, including Estonia's candidacy for a non-permanent seat on the United Nations Security Council in 2020 and 2021.

Bilateral relations important, mutual criticism remains

Both presidents agreed that a lack of connections between neighbouring countries is unhealthy in the long term, and pointed out where cooperation is indeed happening.

At the same time, certain issues remain. President Kaljulaid pointed to the Estonian-Russian border treaty, still not ratified by the Russian parliament, and the controversial Nord Stream 2 gas pipeline.

According to notes prepared for the meeting that were published by news agency Interfax on Thursday afternoon, President Putin takes issue with the lasting "glorification of Nazism" in Estonia, the situation of the holders of Estonian alien's passports and the state of Russian-language education.

Kaljulaid: Headway can be made despite differences

There was no mutual press conference scheduled. President Kaljulaid answered journalists' questions at the Estonian embassy later on, saying that the meeting with President Putin had been "very good".

"We talked for a good while about difficult topics and demonstrated mutual respect even in the most difficult moments," the president told reporters.

Beyond difficulties, there is also room for cooperation, she added. "There are always topics in the relations of neighbours where there is common interest, and where we can do something for the people and for businesses."

The meeting, then, also touched on cross-border cooperation. Both existing as well as planned efforts were discussed, along with options to improve economic relations between the two countries. A specific example in this area could be solving the problem of double taxation, the president said.

President Kaljulaid stressed that both countries are interested in continuing cross-border cooperation also in the next European Union budget period, and that it is "important to find common priorities" these efforts could then concentrate on.

President invites Russian head of state to Tartu

The president told reporters that she would like to invite President Putin to Tartu for the 2020 World Congress of Finno-Ugric Peoples. Political scientist and Karmo Tüür told ERR's Aktuaalne kaamera newscast on Thursday evening that this offer is a very sensible move.

"The invitation is a very elegant move in that the Finno-Ugric theme is something Vladimir Putin has shown interest for in the past," Mr Tüür said, adding that in this sense, the invitation is a "reasonable" way to continue where the meeting left off.

Meeting avoids delicate issue of President Päts chain of office

A delicate issue that remained unmentioned is the chain of office of Estonia's first president, Konstantin Päts. The gold livery collar was lost for a few years following the Soviet Union's occupation of Estonia and the proclamation of the Estonian SSR, but resurfaced in the Kremlin Armoury in 1963.

Russia still hasn't returned the stolen chain of office to Estonia. A replacement was presented to President Toomas Hendrik Ilves on the occasion of the Republic of Estonia's 90th anniversary in 2008.

The chain remains in the Kremlin Armoury, and although Russian officials have on occasion confirmed that there is the intent to give it back to Estonia, there is currently no sign that its status as yet another hostage will change anytime soon.

Asked about the chain, President Kaljulaid said more important issues were discussed at the meeting.