Activists in the new movement vowed to fight the amendments, which would become the first changes to Russia's post-Soviet constitution if they pass the upper house and two-thirds of regional assemblies, as widely expected.
"We will be one of the only political movements in Russia to stand in defence of the constitution," Ilya Yashin, one of the activists at the meeting, said.
Yashin said that the founders of Solidarity had chosen the name in part because of the 1980s Polish trade union federation of the same name, which pushed the government of the Soviet bloc country to hold free elections in 1989.
"The victory of our Polish colleagues did much to inspire us," Yashin said.
Like the original Solidarity, the new movement plans to push for greater democracy, Yashin said, complaining that "there are no real elections in the country".
Previous attempts to unify the Russian opposition have stumbled due to disagreements over strategy and personal conflict between opposition leaders.