The prime minister spoke with Mr Putin on the sidelines of a Berlin summit on Libya’s long-running civil war, according to a Downing Street spokesperson.
Mr Johnson is also said to have reiterated the UK government’s condemnation of the 2018 Salisbury poisoning, which was allegedly carried out by two spies working for Russian military intelligence.
“He was clear there had been no change in the UK’s position on Salisbury, which was a reckless use of chemical weapons and a brazen attempt to murder innocent people on UK soil,” the spokesperson said.
“He said that such an attack must not be repeated.”
The spokesperson added: “The prime minister said there will be no normalisation of our bilateral relationship until Russia ends the destabilising activity that threatens the UK and our allies and undermines the safety of our citizens and our collective security.”
Mr Johnson met with the Russian president as world leaders gathered to discuss plans to solidify a ceasefire in Libya and help relaunch a political process to prevent further chaos in the north African country.
“We are here for an urgent and pressing reason: to stop Libya’s downward spiral,” Antonio Guterres, the UN secretary-general, told the conference.
Libya has descended into chaos since the 2011 killing of its long-time dictator Muammar Gaddafi.
The country is now divided into rival administrations, each backed by different nations, with a UN-recognised government in Tripoli led by Mr Sarraj, and a government in the east supported by General Haftar’s forces.
“On Iran, the leaders reiterated their commitment to the JCPOA [the official name of the deal] and also acknowledged the need to define a long-term framework to prevent Iran acquiring a nuclear weapon,” the spokesperson said.
“They agreed on the importance of de-escalation and of working with international partners to find a diplomatic way through the current tensions.”
Additional reporting by PA