Sergey Lavrov made the comments to journalists after talks between Ilham Aliyev and Serzh Sargsyan, mediated by Dmitriy Medvedev, in Sochi today, Russian news agency RIA-Novosti reported.
He also said that Russia had agreed to a request from Azerbaijan and Armenia to mediate in the establishment of public contacts between the countries.
"The sides registered mutual understanding that further progress - and this is evident - requires a step back from maximalist positions, and the Armenian and Azerbaijani presidents, with the support of Dmitriy Medvedev, expressed this," Lavrov told journalists after the meeting.
He said the three presidents had discussed "the full range of issues which remain unresolved in the draft Basic Principles of a Nagorno-Karabakh resolution".
The presidents "exchanged views on specific complex themes and the conclusion was drawn that the work should be continued".
"The participants in the meeting expressed readiness to speed up work on general principles in order to move, on their basis, to drafting a legally binding peace agreement," the Russian foreign minister said.
He said that as a mediator and one of the OSCE Minsk Group "troika" Russia "will continue efforts to bring the positions of the sides closer".
The three presidents issued a statement after the meeting in which they said that "a result of intensive negotiations progress had been made in reaching agreement on the Basic Principles of a Nagorno-Karabakh settlement".
Public diplomacy
The Armenian and Azerbaijani presidents asked Russia to mediate in the establishment of humanitarian ties between the two countries, another issue raised in the presidents' statement after the meeting.
"Baku and Yerevan asked Russia to initiate such contacts," Lavrov said. "Dmitriy Medvedev of course agreed."
He said that Russia had always supported humanitarian ties.
The three presidents "expressed their conviction of the need for direct humanitarian, cultural, educational and other contacts between people", Lavrov continued.
They "recognize that such contacts play an important role in "restoring and reinforcing trust between Armenia and Azerbaijan and creating an atmosphere as conducive as possible to the adoption of political decisions".
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