* This content was produced in Russia, where the law restricts coverage of Russian military operations in Ukraine.

MOSCOW, July 5 (Reuters) - Russia's parliament backed a bill on Tuesday providing for jail terms of up to eight years on those found to cooperate in secret with international organisations, part of a package of new "crimes against state security".

Russia has already branded political opponents of President Vladimir Putin "extremists" and shut them down and jailed their leaders. Many dissidents have fled into exile during the crackdown, which has intensified over the past two years. Russia's most prominent human rights group was shut down this year for failing to properly register as a foreign agent.

Since sending troops into Ukraine in February, Moscow has further restricted dissent, including imposing jail terms of up to 15 years for reporting that diverges from official accounts of its "special military operation". Virtually all independent media have since been shut.

The package of amendments to the criminal code, which passed its second of three readings in the State Duma lower house on Tuesday, would impose a sentence of up to eight years for "confidential cooperation" with foreign organisations, or sharing information that could be used against Russia.

It introduces a maximum four-year term for "repeated public demonstration of symbols of Nazism and extremist organisations".

Russians who take part in military action "contrary to the interests of the Russian Federation" could be jailed for up to 20 years.

The bill would "improve the effectiveness of the system for detecting, preventing and suppressing criminal activities carried out to undermine the foundation of the constitutional system, the country's defence capabilities and state security", an explanatory note attached to it says.

In recent years, Moscow has applied the "extremist" label to the Anti-Corruption Foundation of Putin's most prominent political opponent, Alexei Navalny. Other organisations banned as extremists include the Jehovah's Witnesses, and groups linked to ethnic Crimean Tatars that oppose Russia's 2014 annexation of the peninsula. (Reporting by Reuters; Editing by Kevin Liffey and Peter Graff)