Church and state are closely linked in Russia and it is unlikely that the Patriarch would have spoken without being confident of backing from the country's political rulers.
The Patriarch made his comments in Red Square, reminding reporters that krasny, the Russian word for "red", originally meant "beautiful".
"This beautiful square, in the city centre, has been turned into a cemetery," he said, adding that rock concerts were sometimes held within yards of where the dead were at rest.
This was not right, he said, expressing the hope that "in time" they would have an appropriate "pantheon".
Commentators noted his tactful tone on this still-divisive issue, but clearly he was trying to introduce to the older generation of committed Communists the idea that their idol might one day be buried in the ground like any other mortal.
Vladimir Lenin, the founder of the Soviet Union, died in 1924. Before his death, he expressed a wish to be buried alongside his mother in St Petersburg. But for political reasons, Stalin needed to maintain the cult of Lenin, so he had the body embalmed and displayed in the red marble mausoleum. Teams of scientists regularly treated Lenin's body with preserving chemicals and even exported their unique technique to other Communist countries, where revolutionary heroes were similarly embalmed. Many Russians, however, find the whole business distasteful.
President Boris Yeltsin undoubtedly shares their view. He has removed the guard of honour from outside Lenin's mausoleum, and it is believed that he would like to see Lenin buried before he completes his presidential term in 2000.