There have been a spate of major demonstrations on college campuses from California to Massachusetts over the past week
Since he divorced his wife Ludmila in 2013, rumours have swirled around Putin.
One Russian newspaper report said he was in a relationship with Alina Kabaeva, a former Olympic gymnast, though Putin rejected the assertion.
During a televised phone-in, an annual event where Putin fields questions from ordinary Russians, one woman asked Putin if he was going to re-marry.