The Sunday Times newspaper reported Al-Qaeda plotted to murder the entire Australian team in their change rooms during the Edgbaston Test in Birmingham, using sarin nerve gas sprayed by the men who bombed the London Underground.
"We are totally confident in the security precautions Cricket Australia and the Australian Cricketers' Association (players' union) take on our behalf," Ponting said in a statement released in India, where the team is about to play in the Champions Trophy tournament.
"Cricket Australia and the ACA have a track record of keeping us informed and acting on security information when and if the situation warrants."
"With regards to this report, we were very comfortable with the security arrangements that were in place during the recent Ashes tour and we continue to trust the security information provided to us by Cricket Australia and the ACA."
However, Ponting did raise his concerns over security on the tour in the wake of the London bombings in July last year, which killed 52 people on underground trains and buses.
"I know quite a few players feel there is an element of inconsistency about our decision to continue with the tour and I agree with that," Ponting wrote in his Ashes Tour Diary.
"If we were in, say, Pakistan or Sri Lanka and something like this had happened, I am sure we would have been on the first plane out."
The Sunday Times said a friend of one of the four London bombers had told the newspaper that an Al-Qaeda cell was initially ordered to kill the England and Australian cricket teams during the Edgbaston Test.
The friend - whose real name was not published - said the attack may have been called off and the Tube bombings planned instead because one of the bombers, Shehzad Tanweer, was a cricket fan.
British and Australian authorities have been unable to confirm the claims, but The Australian newspaper said Monday agencies in both countries were launching investigations to check the information.
The man cited in The Sunday Times story said he would cooperate with police.
A Cricket Australia spokesman said Monday team management had worked closely with security chiefs and the London Metropolitan police in the aftermath of the London bombings, and had not heard any reports that the teams were targeted.