Echoing the claims of other opposition leaders, he described as "genocide" the security forces' treatment of demonstrators who took to the streets after parliamentary polls last weekend that the opposition says were rigged.
The police kept a low profile on the square but were massed in large numbers nearby.
Dozens were injured and hundreds arrested in last week's rioting, which was sparked by claims of vote-rigging at the parliamentary polls.
The vote was officially won by Voronin's Communist Party, with 60 out of the 101 seats in parliament.
One of Europe's poorest states, Moldova remained outside the Western course of many central and east European states after the 1991 Soviet collapse, held back by its complex 20th century history and a separatist conflict.
The new parliament is to decide on a new president to replace Voronin.
On Friday Voronin called for a vote recount to allay concerns, but the move was dismissed by the opposition who say the problems with the vote lay elsewhere, such as the inclusion of many long-dead residents on voter lists.