The State Duma voted 375-2 in favor of the measure, which also carries prison terms of up to eight years for illegally obtaining secret state information.
Current legislation defines high treason as espionage or other assistance to a foreign state damaging Russia's external security.
The new bill expands it to include moves against Russia's "constitutional order, sovereignty, and territorial and state integrity."
The bill, drafted by the Federal Security Service (FSB), also changes the interpretation of treason to include "granting financial, technical, consulting or other help" to a foreign state or an international organization.
It also mentioned unspecified attempts by various international organizations to obtain Russia's state secrets "by illegal means."
The proposal adds multinational organizations to a list of bodies that could benefit from state secrets. Previously the list had only named the governments and organizations of foreign states.
Moscow ordered the U.S. Agency for International Development (USAID) to close at the start of this month, accusing Washington of using its international aid mission in Russia to meddle in Russian politics and influence elections.
The opposition Just Russia party said it opposed the changes, saying such a wide definition of high treason meant "almost any Russian citizen with any contacts with any foreigner" could be accused of betraying the state.
Russia's Human Rights Ombudsman Vladimir Lukin, who was appointed by President Vladimir Putin, sided with the bill's critics.
Lukin said the measure contradicted international law and Russia's constitution by giving a definition that was too broad to fairly determine an individual's guilt.
Pavel Chikov, who heads the Russian human-rights group Agora, told RFE/RL's Russian Service in Moscow that complaints addressed by Russians to international bodies can now be viewed as "high treason."
"A complaint to the UN Commission on Human Rights or the European Court of Human Rights, for instance, which contains information that may appear to the FSB as threatening Russia's national security, is essentially high treason now."
With the October 23 approval from the lower house, the bill is all but certain to be approved by the upper house of parliament before it goes to Putin to be signed into law.