Six were shot dead in the capital Kinshasa, at least three in the central town of Tshikapa and others in the party stronghold of Mbuji-Mayi on Thursday, Joseph Mukendi, an aide to the leader of the Union for Democracy and Social Progress (UDPS), said.
"We have identified 10 people shot dead across the country, while others remain to be confirmed," he said, adding "there were dozens wounded".
The UDPS had called for a peaceful rally to protest delays in holding elections that were originally planned for 30 June under a pact to end a ruinous five-year civil war but put off for at least six months by parliament.
Police have said at least one person was killed and probably more as they dispersed gatherings in various districts of Kinshasa after the authorities banned the marches.
Some 1000 people backing Congo's main opposition party, the UDPS, demonstrated outside the US Embassy and attempted to march to European Union headquarters and Congo's embassy in the city, demanding elections go ahead.
Riot police and two water cannons were used to ensure the demonstrators did not make their way to the EU quarter.
"We have identified 10 people shot dead across the country, while others remain to be confirmed"
aide to the leader of the Union for Democracy and Social Progress
Several parked cars on the street were damaged as violence erupted between police and demonstrators.
A similar protest last week caused damage to the Congolese embassy and led to talks between the opposition group and Belgian Foreign Minister Karel De Gucht.
Meanwhile, the Belgian Senate also debated the situation in Congo and called for calm in the former Belgian colony.
Urgent election calls
The Senate called for the "urgent organisation of elections which should be monitored by EU observers".
The long-awaited presidential elections were to have been held on Thursday, according to a 2003 peace accord between the government in Kinshasa and rebels agreed to at the end of Congo's five-year war.
However, the commitment to hold the vote was pushed back to next year, after the transitional government said it needed more time.
Thursday's protests also coincided with the 45th anniversary of the independence of Congo from Belgium.