Putin, however, has generally ignored opposition demands and avoided giving any ground on controversial issues, apparently seeing it as a sign of weakness. His decision last month to sign a bill banning Americans from adopting Russian children came despite widespread public outrage.
Putin has not weighed in on the hospital controversy.
In Soviet times, Hospital No. 31 provided medical treatment for privileged Soviet bureaucrats. Similar specialized clinics for the Communist Party elite existed elsewhere as well.
During the democratic reforms of the 1980s, the hospital was handed over to the city, with preference to be given to World War II veterans. The children's oncology clinic also was established.
"Twenty years ago it seemed obvious that the privileged St. Petersburg residents were precisely children and elderly people. We hope this is not in doubt now," the petition to Putin says.
Moscow has numerous hospitals that serve the presidential administration or a certain government ministry, a tradition carried down from Soviet times. Today, however, the medical services also are available to other residents on a paid basis.