Johnson made the comments at the start of talks with Russian Foreign Minister Sergei Lavrov during the first visit to Russia by a British foreign minister in five years. Johnson was expected to meet Kremlin critics, students and gay rights activists later on Friday.
His visit comes at a time when relations between London and Moscow are strained by differences over Ukraine and Syria as well as by allegations, which Russia flatly denies, that Moscow has meddled in the politics of various European countries and backed cyber attacks and disinformation campaigns.
"Our relations with Russia cannot be 'business as usual' whilst Russia continues to attempt to destabilise European states, including Ukraine," Johnson said in a statement released by his office before the talks.
Lavrov told Johnson at the start of the talks that British-Russian relations were at a really low point, and "not due to our actions".
"You and other Western colleagues have your views on why this situation exists and prefer to set out these reasons publicly. We wanted to discuss our mutual concerns directly," said Lavrov.
Johnson told reporters before the visit that Britain disapproved of many things that Russia had done. He singled out its 2014 annexation of Crimea from Ukraine, and its cyber activities.
But Johnson also stressed his desire for London and Moscow to cooperate where they have common interests, saying it was vital for international security that the two countries talk to each other rather than risk dangerous misunderstandings.
Russian Foreign Ministry spokeswoman Maria Zakharova said before the visit that the decision to scale back British-Russian dialogue had been London's, and had been groundless and untimely.
Johnson riled Russian officials before his visit by saying Moscow was "closed, nasty, militaristic and anti-democratic" in an interview with Britain's Sunday Times newspaper.
Zakharova said Russian officials had not taken offence, but merely laughed because the comments had been made by Boris Johnson.
(Reporting by Andrew Osborn Additional reporting by William James in London; Editing by Kevin Liffey)
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