Mr Gore broke his silence over the issue to accuse the president of squandering the good will of the world towards America.
He said war against Saddam Hussein would detract from the main US pursuit of those who killed more than 3,000 Americans on 11 September 2001.
Mr Gore's remarks were similar to those made by a panel of retired four-star American generals testifying before a Senate committee as the US Congress prepares a resolution to authorise attacks on Iraq.
Gore's assault
The BBC's Justin Webb says Mr Gore, who has in the past backed the ousting of Saddam Hussein, is now accusing Mr Bush of trying to replace international law with the notion that there is no law but the discretion of the president of the United States.
"I don't think we should allow anything to diminish our focus on the necessity for avenging the 3,000 Americans who were murdered and dismantling that network of terrorists that we know were responsible for it, " Mr Gore told an audience in San Francisco.
"The fact that we don't know where they are, should not cause us to focus instead on some other enemy whose location might be easier to identify."
"Great nations persevere and then prevail, they do not jump from one unfinished task to another."
Mr Bush's Republicans were horrified by the speech - a party spokesman called it "more appropriate for a political hack than a presidential candidate".
Generals warn
Mr Bush is hoping to get broad backing from Congress within the next two weeks for a possible military strike and Mr Gore's intervention might well embolden those Democrats who want to limit the powers they grant the president, our correspondent says.
On Monday, the Senate armed services committee heard testimony from a panel of retired generals - some advancing similar arguments to Mr Gore's.
Former Nato supreme European commander, Wesley Clark, said that "by lumping the two together - al-Qaeda and Saddam Hussein - it is also possible we will have incentivised Saddam Hussein now as a last-ditch defence to do what he wouldn't have done before, which is ... well find me the nearest members of al-Qaeda, here take this sack and do something with it".
General Joseph Hoar, former Commander in Chief, US Central Command, said that although he remained in favour of regime change in Iraq, the first priority for the US "has got to be al-Qaeda".
But former Chairman of the US Joint Chiefs of Staff General John Shalikashvili saw both issues as closely linked.
"The war against terrorism is our number one priority and considering using force to do away with the weapons of mass destruction in Iraq is a necessary part of that war."
All the generals urged Mr Bush persevere with the task of getting authorisation from the UN Security Council for any action in Iraq.