The two leaders discussed issues including climate change and Afghanistan in a phone call.
“The Prime Minister was clear that the UK’s current relationship with Russia is not the one we want,” a Downing Street spokesman said.
“He said significant bilateral difficulties remain, including the poisonings in Salisbury in 2018.
The Prime Minister also underscored the importance of Ukrainian sovereignty.
“The Prime Minister said that as fellow permanent members of the UN Security Council and major world economies with a long, shared history, the UK and Russia have a responsibility to work together to tackle shared challenges like climate change and safeguard international agreements like the Iran nuclear deal.”
On Afghanistan, Mr Johnson “stressed the importance of any recognition of the Taliban being conditional on their behaviour, including respect for human rights”.
The Prime Minister and the Russian president spoke ahead of the Cop26 summit in Glasgow which Mr Putin will not attend.
Mr Johnson welcomed a Russian decision to commit to reaching net zero greenhouse gas emissions by 2060 but pushed for more action.
“The Prime Minister expressed his hope that Russia will raise that target to achieving net zero by 2050 as well as making further progress on ending deforestation and an ambitious nationally determined contribution.
“President Putin expressed his regret that he would not be able to attend the Cop26 Summit in person in the light of the coronavirus situation in Russia.”