The protest rally started in Simono Daukanto Square at noon and was to be followed by a march to the government building.
"We demand that poverty and inequality be reduced," a banner read.
Pensions increased in early January as a result of indexation and certain changes in how pensions are calculated. The average monthly old-age pension is planned to reach around 332 euros this year, up by 30 euros from late 2017.
However, Bočiai is calling on the ruling Lithuanian Farmers and Greens Union (LFGU) to deliver on their election promise to increase pensions by 40 euros.
LFGU Chairman Ramūnas Karbauskis said that the protesters' demands were legitimate.
"We are doing our best and will continue to do our best to further increase pensions," he said, adding that the prime minister would unveil more details "shortly".