The law as passed by the House and Senate requires government agents to get warrants to open first-class letters.
But the presidential statement, signed on December 20, added that sealed mail can be searched in "exigent circumstances, such as to protect human life and safety against hazardous materials, and the need for physical searches specifically authorized by law for foreign intelligence."
The White House said the president is not claiming any new authority and that the statement does not change the scope of current law.
Spokeswoman Emily Lawrimore told CBS News White House correspondent Mark Knoller, "The signing statement merely recognizes a legal proposition that is totally uncontroversial: that in certain circumstances – such as with the proverbial 'ticking bomb' – the Constitution does not require warrants for reasonable searches."
But CBS News legal analyst Andrew Cohen questioned why the president felt it necessary to attach the language to the bill if nothing has changed.
"I don't think the White House would have included this language into a signing statement unless the feds were either already searching mail without a warrant or planning to do so," Cohen said. "And if the legal right to do so were as clear as the White House now says it's hard to believe that there was a need to remind everyone of the fact in a bill about the postal service."
"The signing statement raises serious questions whether he is authorizing opening of mail contrary to the Constitution and to laws enacted by Congress," said Ann Beeson, an attorney with the American Civil Liberties Union. "What is the purpose of the signing statement if it isn't that?"
She said the group is planning to file request for information on how this exception will be used and also asking whether it has already been used to open mail.
Postal Vice President Tom Day said Thursday: "As has been the long-standing practice, first class mail is protected from unreasonable search and seizure when in postal custody. Nothing in the Postal Accountability and Enhancement Act changes this protection. The president is not exerting any new authority."
However, Sen. Charles E. Schumer, D-N.Y., criticized Bush's action.
"Every American wants foolproof protection against terrorism. But history has shown it can and should be done within the confines of the Constitution. This last-minute, irregular and unauthorized reinterpretation of a duly passed law is the exact type of maneuver that voters so resoundingly rejected in November," Schumer said.
The White House first came under in December 2005 when the New York Times revealed a National Security Agency program which eavesdropped on phone calls without warrants to do so.
Mr. Bush claimed the NSA program is needed in the war on terrorism; opponents say it oversteps constitutional boundaries on free speech, privacy and executive powers.
In October, a federal appeals court after a lower court had ordered it stopped.
President Bush has also come under fire from legal experts for creating or expanding presidential powers in bill signing statements. In July, an American Bar Association task force said that the .
"If left unchecked, the president's practice does grave harm to the separation of powers doctrine, and the system of checks and balances that have sustained our democracy for more than two centuries," ABA president Michael Greco said at the time.
Bush has issued at least 750 signing statements during his presidency, more than all other presidents combined, according to the ABA.
Typically, presidents have used signing statements for such purposes as instructing executive agencies how to carry out new laws.
Bush's statements often reserve the right to revise, interpret or disregard laws on national security and constitutional grounds.
Both the warrantless searches and the president's use of signing statement's could be challenged by the newly convened Democratic congress.
"With Democrats now in control of Congress, don't be surprised if we see an investigation into these sorts of uses of signing statements and of the White House's legal authority to undertake searches like this without a warrant or other court order," Cohen said.