The leaders of Britain and Russia held a rare phone call on Monday before the Cop26 summit, with London expressing frustration at the tense state of relations.
Russian President Vladimir Putin said he regretted being unable to attend the UN climate summit starting next week in Glasgow, UK Prime Minister Boris Johnson's office said.
Mr Johnson hoped that Russia would take more ambitious steps towards curbing carbon emissions and ending deforestation, the office said.
"The prime minister was clear that the UK's current relationship with Russia is not the one we want," his office said. "He said significant bilateral difficulties remain."
Downing Street highlighted the 2018 poisoning of Russian former spy Sergei Skripal in Salisbury and the conflict in Ukraine.
British police say three members of Russian military intelligence carried out a nerve agent attack in March 2018 in the English cathedral city.
While Skripal and his daughter recovered, a local woman who came into contact with the nerve agent, Novichok, later died.
Relations between Britain and other western countries and Russia were strained over Moscow's 2014 annexation of Crimea from Ukraine, and they accuse the Kremlin of continuing to support separatists in the country's east.
The Kremlin said Mr Putin and Mr Johnson agreed that: "Despite the existence of known problems, it would be necessary to establish co-operation between Moscow and London in a number of areas."
Downing Street said Mr Johnson stressed that London and Moscow had a "responsibility to work together" on issues including the Iran nuclear deal.
The two leaders last spoke in May 2020, marking the 75th anniversary of the end of the Second World War in Europe.