The Prime Minister held talks with the Russian President in Berlin during a world leaders' summit hosted by German Chancellor Angela Merkel.
The two leaders met at the international conference to discuss the situation in Libya.
Mr Johnson told the Russian leader there would be no change in the UK’s stance towards Russia until it ended the "destabilising activity" that threatens the UK.
A Downing Street spokesman said: “The Prime Minister met President Putin in the margins of the Berlin conference on Libya.
“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.
“He said that such an attack must not be repeated.
“The Prime Minister said that they both had a responsibility to address issues of international security, including Libya, Syria, Iraq and Iran.
“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.”