Bribery, Doping killing world athletics — Pound
Lord Coe says public trust in athletics may not return until "way beyond" his four-year term as IAAF president.
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Last Thursday, a World Anti-Doping Agency independent report said "corruption was embedded" within the governing body.
Its author, Dick Pound, said some athletes from Russia and Turkey who failed drugs tests then paid bribes.
"If there are athletes out there and they think they have been subject to extortion, come and speak to me," Coe told BBC
"We need to understand how far and how wide this thing goes. If it's the tip of the iceberg, then come forward and make those claims."
The report said corruption within the IAAF "cannot be blamed on a small number of miscreants" and its council, which included Coe, "could not have been unaware of the extent of doping in athletics".
The report was heavily critical of the IAAF, but Pound said he "could not think of anyone better" than Coe to lead reform.
Britain's double Olympic 1500m champion, who was elected president in August after eight years as vice-president, said he wants to be "unflinching in the changes that we make".
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But he added that, at the end of his term as president, "I don't necessarily think the public will be sitting there being trustful about everything that we've done".
'I did not have a charge sheet'
Coe succeeded Lamine Diack as IAAF president
The Wada independent report said former IAAF president Lamine Diack was "responsible for organising and enabling the conspiracy and corruption that took place in the IAAF".
Diack is being investigated over allegations he took payments for deferring sanctions against Russian drugs cheats.
His son, Papa Massata Diack, has been banned for life from the sport and is the subject of a French police 'wanted' notice issued via Interpol on charges of corruption and money-laundering.
When Coe was elected president, he said of his predecessor: "He will always be our spiritual president and he will certainly be my spiritual president."
Asked about those comments, Coe said: "I didn't know then that all this was about to surface.
"This is a person who had globalised the sport to 214 countries. It was a strong sport. These were the observations I was making. I did not have a French prosecution charge sheet.
"I am not going to sit here and say I would have made the same remarks if I had known the extent of the allegations."
Asked if he had any suspicions about Diack, Coe replied: "No, absolutely not."
'I didn't have a full focus on athletics'
Russia was suspended from athletics last November after Pound, in the first part of his report, accused it of "state-sponsored doping".
Coe said the IAAF council was aware Russia "was becoming an escalating problem" and there were discussions "at president-to-president level".
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He added: "We should have been able to go back and say: 'What happened when those conversations were taking place? What was the outcome?'
"When corruption takes place, it's rare that it's shared with co-workers."
The 59-year-old joined the IAAF council in 2003 but said he was only able to have a "limited focus" on the sport while he was chairman of the London 2012 organising committee.
"For 10 or 11 years, I was extremely busy in bidding or delivering a London Games," he said. "I didn't have the advantage of having a single focus on athletics."
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Will Russia return for Rio 2016?
Coe said Russia would only be readmitted to international competition "when we think they are in a position to deliver safe and secure systems to their athletes and not a moment before".
He added: "What we've said to them is, 'your clean athletes will only be appearing in international competitions again when we are entirely satisfied that you have done what we have asked you to do'. We haven't set artificial barriers. We haven't set easy, attainable targets.
"Wada has to make sure Russia's anti-doping is compliant as well."
Asked whether that would be before this summer's Rio Olympics, he said: "We're not saying that - let's see where we get to before we put an artificial time limit on it."
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On Saturday, Russia named Dmitry Shlyakhtin as the new head of its athletics federation. He said: "Going to the Olympic Games is task number one."
'I will change athletics within four years'
Coe said his "biggest challenge" is restoring the public's trust in athletics, but added: "It may be the case that the trust has not returned way beyond my term."
He added: "For the sport to believe, fundamentally, that clean athletes are in a position to deliver their God-given talents on a clean platform will take longer. This is not an exact science.
"The challenge is in two key areas. One is to change the corporate governance, the way we do business within the sport, within the federation. The other is to return trust back to the track and that is primarily and overwhelmingly a simple principle - it is to get the cheats out of the sport as quickly as we can."
Coe said he would make the changes "well within four years".
'I have answered every question'
Coe was asked whether he would be willing to take a lie-detector test to prove he was telling the truth about his time working at the IAAF.
He said: "I have answered every question. With all due respect, I am answering questions virtually every hour of the day in virtually every forum."