In the first challenge to his FIFA post in 13 years, the 60-year-old Qatari beat Sheikh Salman bin Ebrahim al-Khalifa of Bahrain 23-21 in a ballot of Asian Football Confederation (AFC) members to retain the seat having said he would step down as AFC president if defeated.
The election campaign was marked by name-calling and accusations of dirty tricks, with FIFA vice-president Chung Mong-joon saying Bin Hammam had mental problems.
The Qatari, in London to speak at the Soccerex Forum at Wembley, said he did not intend to let the matter rest.
"I think everyone has a job to investigate these allegations," he told reporters. "If they are wrong, let them blame me."
Asked if he thought FIFA's ethics committee should get involved, he said: "I invite them, I urge them and I wish they are going to go ahead and investigate.
"In the election I won by 23 to 21 votes, with two disqualified, which were both for me.
FIFA FAILURE
"I can assure you that at least 10 national associations did not vote for me because of the interference of their Olympic Committee and their bad behaviour. If I had been talking directly to the national associations I should have (had) more than 35 votes."
Addressing the Forum, a gathering of hundreds of "stakeholders" in the business of football", Bin Hammam said FIFA had failed in its duty.
"I believe the world of football needs to enhance its independence. I think FIFA failed this time to protect the interest of football," he said.
"National Olympic committees in Asia have a lot of influence. I have evidence that some of the votes were changed in the last 24 hours before voting."
The election and its fallout have caused a deep rift in the region and despite his call for an inquiry, Bin Hammam recognised that bridges needed to be built.
"It is my duty now as leader of football in Asia to bring people together and do my job to make sure that the football associations are very much independent," he said.
"The people in Asia have witnessed a tough and democratic competition. Inside the boardroom the environment was quite healthy, outside maybe it was played a little bit unfairly.
"(Attempts to buy votes) took place but we will overcome these bad acts and will be able to conduct our elections in a better way."
