The US is calling on Nigeria to prosecute people who intimidated voters and tried to stop them casting their ballots in last weekend's governorship and state assembly elections.
Its embassy says there was evidence of this happening in Lagos, Kano, and other states and that "the use of ethnically charged rhetoric before, during, and after the gubernatorial election in Lagos was particularly concerning".
Similar concerns were voiced by EU observer mission chief Barry Andrews, who said Lagos was among several states troubled by violence, ballot snatching and the intimidation of voters, election officials, observers and journalists.
At least 21 people were killed in the violence, the EU says.
These latest polls come three weeks after a contentious presidential election, which at least one opposition leader is now challenging in court.
Nigeria's two biggest political parties, the governing APC and the main opposition PDP, have won control of most of the states in the governorship election. But there were some upsets.
The New Nigeria People’s Party, formed just months to the poll, defeated the APC to win the governor seat in Kano - the economic hub of the north.