President Muhammadu Buhari said “only fiends from the nether region” could have done this “dastardly act”.
The armed men entered St Francis Catholic church in the town of Owo during a Sunday service. They fired into the congregation and then kidnapped a priest as well as some other church-goers, witnesses said.
Nigeria has experienced an upsurge in violence in recent months.
Kidnappings and attacks have been reported across the vast country.
No figures for the numbers killed or abducted in Sunday’s violence have been confirmed.
But a doctor at a local hospital, quoted by the Reuters news agency, said that “several worshippers were brought in dead”. After visiting the church and hospital, state lawmaker Ogunmolasuyi Oluwole told the Associated Press news agency that children were among the dead.
In a series of tweets, Ondo state Governor Rotimi Akeredolu called it a “vile and satanic attack” on innocent people. He appealed for calm, urging people not to take the law into their own hands.
“The assailants will be hunted down and they will pay for their crimes,” he added in a message sent after being briefed at the scene.
“No matter what, this country shall never give in to evil and wicked people,” President Buhari said in a statement. He is in the final year of his two-term presidency and has been criticised for failing to get to grips with the country’s security problems.
No one has said that they were behind this attack, but Nigeria is facing worsening violence by armed groups, the BBC’s Chris Ewokor in the capital, Abuja, says. But Ondo state has, until now, been relatively untouched.
Exactly a week ago the head of the Methodist Church in Nigeria was abducted along with two other clerics in the southeast of the country.
The Methodist prelate said he paid $240,000 (£190,000) to be freed with his companions.
Two weeks ago, two Catholic priests were kidnapped in Katsina, President Muhammadu Buhari’s home state in the north of the country. They have not been released.
In March, gunmen targeted the vital rail link between Abuja and the northern city of Kaduna killing at least nine people and kidnapping dozens of others, many of whom are still being held.