In a memorandum addressed to Dmitry Medvedev, which coincided with the organization's annual global report, Amnesty acknowledged improvements in criminal law, prison conditions and prosecutions of judicial officials.
But the group said "a number of serious patterns of violations persist and in some cases have worsened in recent years."
"Amnesty International looks to you as the president of Russia to initiate a sea-change in direction in terms of freedom of expression in Russia," the memorandum said.
Medvedev, a 42-year-old former lawyer, took office in May. He is considered a more liberal politician than his predecessor, Vladimir Putin, who stayed as prime minister.
As president, Putin was credited in his country for presiding over economic and political revival after a post-Soviet chaos, but criticized by Western states for backtracking on democracy.
Amnesty International criticized Russia for strict media control and arrests of protestors, human rights activists and political opponents, some of whom have been subject to beatings. The latest incidents were reported before and after the parliamentary and presidential elections in December and March, which saw an overwhelming victory for pro-Kremlin parties.
"Amnesty International considers it vital in this context to ensure the protection of the right to freedom of expression as one of the cornerstones for the overall protection of human rights," the report said.
Other concerns expressed by the rights organization included growing racist violence and rights violations in Russia's North Caucasus.
