Putin's overture was the latest in a series of contacts with Washington with whom Moscow is keen to rebuild relations frayed over everything from election hacking allegations to Syria.
Putin and Trump say they worked closely together to clinch a global oil production cuts deal and spoke by phone on Thursday when Trump offered to supply Russia with medical equipment to help fight the new coronavirus.
Ties with London remain badly strained over the poisoning of a former Russian spy and his daughter in England. Russian Foreign Minister Sergei Lavrov spoke to his British counterpart Dominic Raab on Wednesday when, according to Moscow, they agreed to try to improve cooperation.
The telegrams were among many Putin dispatched to the Soviet Union's World War Two allies on the 75th anniversary of the end of the conflict in Europe.
Russia, which marks the unconditional surrender of Nazi Germany on May 9, the day after "Victory in Europe" Day, has been forced to scale back commemorations due to the coronavirus.
In the message to Trump, Putin said Russia and the United States now stood at the forefront of confronting global challenges. "Our countries could do a lot to ensure international security and stability," he said.Putin told Britain's Johnson the allies' togetherness during World War Two was needed today and that the memory of those years could help British-Russian ties improve.