The man, who claimed he had been in contact with the Islamist attackers inside the Westgate shopping centre, also said the militants would not negotiate an end to the siege.
The man, who called himself Abu Omar, was speaking to BBC radio after several British newspapers reported that Samantha Lewthwaite, the widow of one of the suicide bombers in the 2005 attacks on the London transport network, could have masterminded the attack.
"I can confirm to you that none of that is true, I know that is baseless rumours that have no justification for them."
He claimed that women would never be involved in perpetrating such attacks.
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"To verify, we do not employ our sisters to carry out military attacks of this type so these are just baseless rumours that have no substance to them," he said.
The man added: "There will be no negotiations."
"We've spoken to the mujahid inside Westgate and they told us that the Kenyan government was urging them to negotiate and was also giving them some incentives to come to the dialogue table.
Heavy gunfire and loud explosions were heard at the mall today as Kenyan troops fought Islamist militants who were still holding hostages.
The siege has so far left 69 people dead, with another 63 missing, according to the Kenyan Red Cross.