The gunmen, reportedly dressed in military-style clothing, attacked the villages of Dekara, Gidan Zana, Sabon Gida and Masaka.
Police spokesman Wasiu Abiodun told the BBC that more than 40 people were killed, but the exact number of deaths had not been confirmed.
Looking at the footage released on social media, the local youth leader, who asked not to be named, said he recognised several individuals from his community.
“I was able to identify many people. There is an elderly man in the video who is like a grandfather to us,” he said. “He lives in Gidan Zana village.”
He said families who had spotted relatives in the video were relieved to know they were still alive.
“At least they know where their loved ones are and hope they may be rescued, unlike those who still have no information about missing relatives,” he added.
A local blogger familiar with the area told the BBC that many residents had fled their homes, seeking refuge in neighbouring states or across the border in Benin.
Some survivors are receiving hospital treatment, including people with serious injuries.
A local official also told the BBC that the attackers planted improvised explosive devices in parts of the affected communities as they led abductees into the forest. He said a teenage boy was killed when an explosive detonated as he tried to escape.
In a statement issued by presidential spokesman Bayo Onanuga, Tinubu condemned the killings and abductions and vowed that those responsible would be brought to justice.
“Those who carried out this cowardly attack on defenceless Nigerians are enemies of peace and enemies of humanity, who will not go scot-free,” the statement said.
The president also expressed his condolences to the families of those killed.
The attack is the latest sign of worsening insecurity in the Borgu area, which borders Kebbi and Kwara states as well as neighbouring Benin.
Earlier this month, police said 145 people had been rescued after being abducted from four other villages in the area.
Local officials have also raised concerns about the growing presence of jihadist groups operating in parts of north-western Nigeria and along the border region, saying some fighters have recently entered communities and imposed religious restrictions on residents.
Additional reporting by Makuochi Okafor
