Fayose said there is no truth in Osinbajo's statement that Buhari is recuperating fast.
He threatened to release 11 of the pictures.
The Governor said Acting President Yemi Osinbajo's statement that Buhari is fast recuperating is a lie from the pit of hell.
Osinbajo, who visited the President in London on Tuesday night, July 11, had upon his return to Abuja on Wednesday said Buhari is recovering quickly and that he may be back in the country "very shortly."
Speaking to newsmen in Abuja on Wednesday, July 12, Fayose insisted on Buhari's resignation, advising him to attend to his failing health.
"If care is not taken, I will release pictures and this will create serious problems for the country. The offices of the governors and the president are that which require work. If care is not taken, I will release about 11 pictures (on his bad health)", the governor said.
Fayose however said he is not praying for Buhari's death.
He challenged Osinbajo to release to Nigerians, pictures or video of his Tuesday meeting with the President.
The Governor added that Osinbajo should honestly tell Nigerians what he saw when he visited Buhari.
He said, "I’m not going to prove that to Nigerians. It is him (Osinbajo) who said he saw the President that needs to prove to Nigerians.
"I have made the allegations and I have said it expressly that we are in the age of technology. So, we have an Acting President of a nation that has visited his boss that cannot show evidence of the meeting.
"The pictures they are posting on social media are pictures taken long time ago. You recall that I said this again at Transcorp Hilton in 2015. We are talking about the President of 170 million people.
"The Acting President visiting the President that has left this country for about 60 days or more cannot show evidence of the meeting. It shows the President is in a critical condition
"I wasn’t saying that we don’t want him to return, but the claim of the acting President is not true. In this age and time when we have the social media, we have everything to show that the government cannot be run by propaganda.
"The fact is, the President is sick, incapacitated and he’s not in good condition. The acting President should show us pictures, short video of his meeting with the President . It is not in the interest of the country that the country will be run in deceit and propaganda.
"The visit (of Osinbajo) was diversionary and an attempt to divert the attention of the country. Both the President and his vice do not have what it takes to run the country.
"As far as it is good to protect the interest of his boss, he should consider the interest of the people. We are no longer credit worthy. We cannot wait for a President that is incapacitated."