"The world's free nations will not allow Iran to develop a nuclear weapon," he said as the US ambassador to the UN nuclear watchdog agency in Vienna said it was time to slap sanctions on Tehran over its atomic activities.
The sharp escalation in rhetoric came as Mr Bush made the second of a series of speeches on the war on terrorism in the run up to November US legislative elections expected to be overshadowed by the unpopular war in Iraq.
It followed the White House's release of a 23-page anti-terrorism strategy that called Iran and Syria "especially worrisome" threats and downplayed the role of the Iraq war and the Israeli-Palestinian conflict in fuelling terrorism.
White House officials denied the president's report and speech were driven by election-year politics, in which President Bush is accusing Democrats of being soft on terrorism, and said the report had been the product of months of work.
In Vienna, the US ambassador to the International Atomic Energy Agency (IAEA), Gregory Schulte, said that "the time has come for the (United Nations) Security Council to back international diplomacy with international sanctions."
Mr Bush made no explicit reference to sanctions in his speech but stressed that: "The world is working together to prevent Iran's regime from acquiring the tools of mass murder."
Quoting Iranian President Mahmoud Ahmadinejad as saying last month that the United States must "bow down" before Iran, the US president fired back: "America will not bow down to tyrants."
Mr Bush accused Iran of funding the Lebanese Shiite militia Hezbollah and other groups in order to attack Israel and the United States "by proxy" and said Tehran aimed to dominate its neighbours.
"Like al-Qaeda and the Sunni extremists, the Iranian regime has clear aims. They want to drive America out of the region, to destroy Israel, and to dominate the broader Middle East," the US president said.
"The Shia strain of Islamic radicalism is just as dangerous and just as hostile to America and just as determined to establish its brand of hegemony across the broader Middle East" as al-Qaeda, he said.
But, he said, Shiite extremists have done something al-Qaeda only dreams of by taking over Iran in 1979, "subjugating its proud people to a regime of tyranny and using that nation's resources to fund the spread of terror and to pursue their radical agenda."
"The Iranian regime and its terrorist proxies have demonstrated their willingness to kill Americans, and now the Iranian regime is pursuing nuclear weapons," Mr Bush said.
Tehran has insisted that it seeks only civilian nuclear power, but has rejected an incentives package from the US, France, Britain, Russia, China and Germany in return for freezing uranium enrichment.
Later, the Iranian ambassador Ali Asghar Soltanieh told AFP that talks set for Wednesday in Vienna between EU foreign policy chief Javier Solana and Iranian negotiator Ali Larijani had been postponed and would be held "in a couple of days".
"We will not have the meeting today (Wednesday) in Vienna but it will be held in a couple of days" in Vienna, ambassador Soltanieh said.
'Not yet safe'
In its report, a reworked version of previous anti-terrorism blueprints, the White House warned that the US was "not yet safe" from terrorism five years after the September 11, 2001 attacks.
It labelled the possible acquisition of weapons of mass destruction (WMDs) by terrorists "our greatest and gravest concern" and said: "Most troubling is the potential WMD-terrorism nexus that emanates from Tehran."
Amid the soaring price tag and rising death toll in Iraq and uncertainty about US efforts to resolve the Middle East conflict, the report downplayed the impact of both crises as sources of anger that fuels extremist violence.
"Terrorism is not simply a result of hostility to US policy in Iraq," it said. "Terrorism is not simply a result of Israeli-Palestinian issues."
In each case, the White House said that al-Qaeda had plotted the September 11 attacks in the 1990s, during an "active period" in Middle East peace talks and well before the March 2003 invasion of Iraq.
However, the report also acknowledged that "the ongoing fight for freedom in Iraq has been twisted by terrorist propaganda as a rallying cry."
Opposition Democrats fired back quickly, with Senator John Kerry, Mr Bush's 2004 rival for the White House, declaring that "We need to change course, not more of the same."
"Afghanistan is slipping back into chaos, Pakistan is one coup away from becoming a radical Islamic state with nuclear weapons, Iran is closer to a nuclear arsenal, and Iraq has become a recruitment poster for terror," he said.