MOSCOW, July 12 (Reuters) - U.S. climate change envoy John Kerry told Russian Foreign Minister Sergei Lavrov on Monday he wanted to set out some proposals to urgently try to get the two big greenhouse gas emitters working together to battle global warming.

In Moscow for talks with Lavrov, President Putin's climate envoy, and government figures, Kerry told the Russian foreign minister that Washington wanted to work with Moscow ahead of the U.N. climate change conference in Glasgow later this year, something Lavrov said Russia wanted too.

Kerry did not publicly say what the U.S. proposals were.

"Obviously, we have some differences in the relationship between our countries but we were very pleased that President Putin took part in the summit," Kerry told Lavrov, referring to a virtual climate summit organised by U.S. President Joe Biden in April.

"We are pleased that Russia wants now to take steps, additional steps, because your country is impacted (by climate change), obviously. And we believe that there is space for us to cooperate on this," he said, adding that climate change in the Arctic was one of many warning signs of the need to act.

Lavrov said he viewed Kerry's visit as a positive signal for bilateral relations and that Russia was hoping for close cooperation on climate issues ahead of the Glasgow meeting.

Kerry said the United States was the world's second biggest greenhouse gas emitter and that Russia was the fourth biggest and that the two nations therefore had a responsibility to act.

Relations between Russia and the United States have been languishing at post Cold War lows since Moscow's annexation of Crimea from Ukraine in 2014 and allegations - which the Kremlin denies - of Russian hacking attacks against the U.S.

Putin and Biden singled out climate change as one of the few issues however where Washington and Moscow could cooperate when they held a summit in Geneva last month. (Reporting by Vladimir Soldatkin Editing by Andrew Osborn and William Maclean)