The Islamic Movement in Nigeria (IMN) Spokesman Ibrahim Musa said the Shia marchers were killed in the northern states of Kaduna, Bauchi, Gombe, Sokoto, and Katsina on Tuesday.
"The Islamic Movement in Nigeria has confirmed the killing of at least a dozen Ashura mourners across the nation during the peaceful Ashura mourning procession today," said Musa.
The group was banned in July after police crackdown on its rallies held to demand the release of its leader. IMN said the police were responsible for the deaths of at least 20 people in July but the police gave no death toll.
Police in the northern city of Kaduna, where IMN said three were killed and 10 injured on Tuesday, disputed the account and said it dispersed marchers "professionally".
A national police spokesman did not immediately respond to a request for comment, according to Al Jazeera.
The group was marching to mark Ashura, the day when Prophet Mohammed's grandson, Imam Hussein (AS), and his companions were martyred in the 680 Battle of Karbala.
Police had warned IMN members not to march, saying any gathering or procession by group members is "ultimately illegal and will be treated as a gathering in the advancement of terrorism".
IMN said police attacked its marchers on Tuesday and, in Katsina, opened fire on them. It said members were killed in Bauchi, Gombe and Sokoto states, all in northern Nigeria, but marches in the capital, Abuja, and other northern states ended without incident.
Clashes with police in the last few weeks followed calls by the group for its leader to be released from police detention.
Their leader, Sheikh Ibrahim al-Zakzaky, has been held since 2015 when government forces killed about 350 people after storming an IMN compound and a nearby mosque.
While roughly half of the nearly 200 million Nigerians are Muslim, mostly concentrated in the north of the country, Shia are a minority.
Last week the United Nations special rapporteur on extrajudicial, summary or arbitrary executions said she had not been presented with any evidence to suggest IMN was weaponized and posed a threat to Nigeria.