Fifa suspended Warner and Bin Hammam over separate allegations of bribery, pending further investigation.
Bin Hammam was suspended by the organisation's ethics committee a matter of hours after withdrawing from the Fifa presidential race on Sunday morning. His decision leaves 75-year-old incumbent Sepp Blatter, who is seeking a fourth term in charge of the organisation he has run unopposed since 1998, as the only man running for the office. Blatter is due to hold a news conference on Monday at 1700 BST.
Fifa has said its election will go ahead, as scheduled, on Wednesday.
Warner, who is president of the North, Central American and Caribbean confederation (Concacaf), has reacted angrily to the allegations of bribery and the Fifa ethics committee's decision to suspend him. The Trinidad and Tobago government minister raged: "I look on the suspension as the worst form of justice by any sporting organisation. "They came premeditated, they weren't prepared to listen, they were hand-picked to do a task and they did just that. "The guys were hand-picked by Blatter. A kangaroo court would be a decent thing to say."
Warner, who also turned on Valcke, stated: "I wrote to Valcke telling him, among other things, that the outcome of the [Fifa presidential] elections may cause some fracture in the Arab world which we can ill afford now and that I will like to ask Bin Hammam to withdraw from the race. "To which Jerome replied to me and I quote: 'For MBH [Mohamad Bin Hammam], I never understood why he was running. If really he thought he had a chance or just being an extreme way to express how much he does not like anymore JSB [Joseph Sepp Blatter]. "Or he thought you can buy Fifa as they [Qatar] bought the WC'."
Warner showed the e-mail to television crews and added: "You don't have to believe me, you don't have to like me, nobody has to eat with me, drink with me or sleep with me but Jesus Christ, take the truth when you see it."
Warner has also accused Blatter of making a gift of computers and an unauthorised $1m (£607,000) to Concacaf officials. "I indicated that at the Miami Concacaf Congress on 3 May Mr Blatter made a gift of $1m to Concacaf to spend as it deems fit," Warner said in a statement. "This annoyed [Uefa] president Michel Platini who was present and he approached secretary general Jerome Valcke complaining that Mr Blatter had no permission from the finance committee to make this gift to which Jerome replied that he will find the money for Mr Blatter. "I also indicated Fifa, through Mr Blatter, organised gifts of laptops and projectors to all members of the Caribbean and no objections have been made today of this to date."
This is the latest in a string of allegations between the men at the top of Fifa.
Warner and Hammam are accused of offering financial incentives to members of the Caribbean Football Union. In a file of evidence it was claimed bundles of cash of up to $40,000 (£24,200) were handed over to members of the CFU at the meeting in Trinidad on 10 and 11 May. The payments were allegedly made to secure votes for Bin Hammam in his campaign to challenge Blatter for the presidency.
Bin Hammam effectively claimed Blatter was aware of some of the wrongdoing but the Fifa president did not report it, in itself a breach of Fifa's ethics code, but he was found to have no case to answer. Warner has also maintained his innocence and denied any wrongdoing.
And last week, Qatar 2022 World Cup officials denied allegations, published in the Sunday Times, that they paid bribes in return for votes.
Meanwhile, independent Australian senator Nick Xenophon has demanded that Fifa refunds the Aus$45.6m (£29.6m) they spent on their unsuccessful bid to host the 2022 World Cup. Xenophon said: "It appears corrupt and highly questionable behaviour goes to the core of Fifa. "Australia spent almost $46m on a bid we were never in the running for. "Now we hear that bribes may have been made to fix the result for who will head up Fifa."
According to the Reuters news agency, China's Zhang Jilong will take charge of the Asian Football Confederation in the absence of Hammam.