Challenger Bin Hammam and incumbent Sepp Blatter, who is running for a fourth term as FIFA president, were guests at the congress of the South American Football Confederation (CONMEBOL) on Sunday where both sat at the top table.
Both men were also present at an asado - South American barbecue - at the ranch of CONMEBOL president Nicolas Leoz on Saturday.
"Let there be a competition, let there be a decision by the (FIFA) congress. Things are on the table, (let's) keep things dynamic and keep the congress always deciding where they are going to go," Bin Hammam told Reuters.
"I think a new vision, a new opening, new blood, the competition in itself is what we are requiring, not change," added the 61-year-old head of the Asian Football Confederation who faces Blatter in the FIFA election in Zurich on June 1.
CONMEBOL, which has staunchly supported Blatter since he took office in 1998, confirmed on Friday that it would back him again on June 1.
Sunday's congress began with a speech by Blatter before 82-year-old Leoz was re-elected for a sixth term as CONMEBOL president, 25 years to the day after the Paraguayan first took over as head of South American soccer's governing body.
"I would like to thank you for the faith you have expressed in FIFA," said Blatter in his address
"I am very happy and honoured with your decision and I accept it gladly... to continue playing together on the same pitch."
CONMEBOL holds 10 of the 208 votes at the FIFA congress.
Bin Hammam addressed the meeting later and quoted from a letter sent to him many years ago by former FIFA president Joao Havelange in which the Brazilian called him a friend and brother.
"In the course of my 24 years' presidency of FIFA I have made many friends but none can compare with your support... you have not only been friend but a brother," Bin Hammam quoted Havelange as having written.
Bin Hammam added: "If I was able to be friend and brother of Havelange, I can be same with you."
However, applause from the floor was only lukewarm.
Asked by Reuters about the reception, Bin Hammam said: "You'll have to ask them why. I have submitted my request to be a friend, there's nothing wrong with that."
Blatter believes he has about 50 percent support from Africa and Asia and a majority in the rest of the world.
Bin Hammam says the issue is not settled.
"I have to (campaign), frankly speaking, and I've said this before, when we first decided to go ahead, we knew where we are strong and where we are weak, and so far I believe none of the decisions has been taken left or right," he said.
"I will not say where my strength is and where my weaknesses are going to be from but I believe that for the election I have time (to garner more support)."
