President Bush warned terrorists around the world on Tuesday that if they attack Americans, they will be hunted down no matter where they hide.

In a tax-policy speech at the Indiana state fairgrounds, Bush denounced Monday night's terrorist attacks in Saudi Arabia that killed at least 29 people, including eight Americans.

"The ruthless murder" of American citizens and others "remind us that the war on terror continues," Bush told a rousing crowd. "These despicable acts were committed by killers whose only faith is hate and the United States will find the killers and they will learn the meanings of American justice … We will be patient. We will be relentless."

The FBI suspects that Usama bin Laden's Al Qaeda (search) terror network is responsible for the attacks, the first of which struck around 11:30 p.m. local time Monday, and constituted the deadliest terror attack on Americans since Sept. 11, 2001.

Terrorists simultaneously shot their way into three housing compounds in the Saudi capital and then set off homicide car bombs. Many Westerners lived in those areas.

"My thoughts and prayers and those of our fellow citizens are with the families of the victims of yesterday's murders in Saudi Arabia," Bush said.

On Sept. 11, 2001, "the enemy hit us, they didn't realize the nature of this country. They thought we would just fold up our tents and go home. They don't understand America, they don't understand how much we love freedom," Bush said during Tuesday's speech.

"Anytime anyone attacks our fellow citizen, we'll be on the hunt and we'll find them and they'll be brought to justice. Just ask the Taliban."

Operation Enduring Freedom (search) helped oust the Taliban from power in Afghanistan and install a new government.

"I'm optimistic we can overcome anything in our path," Bush said. "We have a challenge to make sure we have economic security here at home … we also have a challenge to protect our fellow Americans from terrorism."

White House staff members told Bush about the bombings after he gave a speech on tax cuts, terrorism and the war on Iraq at a plastics manufacturing plant in Omaha, Neb., said White House spokeswoman Claire Buchan. On Air Force One, en route to Indianapolis, Bush received additional information in phone conversations with national security adviser Condoleezza Rice.

On Tuesday morning, the president received an additional update from Rice, along with his daily intelligence briefing.

The FBI is sending a team to the desert nation to investigate the bombings.

John Pistole (search), deputy assistant FBI director for the counterterrorism division, will lead an "assessment team" of a dozen or less agents and technicians, FBI spokesman Bill Carter said Tuesday.

Saudi Arabian officials have already given the team permission to participate in the investigation. The FBI has a permanent legal attache in Riyadh who acts as a liaison with that nation's police and counterterrorism officials.

Investigators will interview witnesses and gather evidence alongside Saudi police, while bomb technicians will try to determine what explosives were used, how they were detonated and how to trace their origin.

Additional FBI agents could be sent to Riyadh depending on the findings of this initial team, as long as Saudi Arabian officials allow it.

Officials don't think the bombings were aimed to coincide with Secretary of State Colin Powell's trip to Saudi Arabia Tuesday.

Powell, in the Mideast for previously scheduled meetings, learned about the bombings when he was awakened around midnight in Amman, Jordan. In the Saudi capital of Riyadh, Powell on Tuesday called the bombings an act of cowardice and said they bore the "earmarks of Al Qaeda."

But U.S. officials say they're pleased with the Saudi crackdown on terrorism, which has forced Al Qaeda to focus on soft targets like apartment buildings rather than embassies and military bases.

U.S. lawmakers took turns condemning the attacks and noted that Al Qaeda is far from obliterated.

Sen. Jon Kyl, R-Ariz., chairman of the Senate Judiciary Subcommittee on Terrorism, Technology, and Homeland Security, called the bombings "a painful moment in our long war against terrorism. Al Qaeda, which some suspect may have been behind this attack, has suffered serious setbacks, but is still a potent enemy."

"Our recent successes in Iraq, Afghanistan and in the global dismantling of terrorist cells may have understandably encouraged some Americans to begin to turn their attention away from the war on terror toward other pressing concerns," Kyl said. "Today's attack is a reminder that our enemies will not be similarly distracted."

Sen. Russ Feingold, D-Wis., said during a speech on the Senate floor Tuesday that the Bush administration is essentially "losing its focus" in the war on terror.

While not quite as strong as the speech Sen. Robert Byrd, D-W.Va., made last week hammering Bush for what he described as "flamboyant showmanship" in the photo-op on the USS Lincoln, Feingold suggested that the administration is too focused on rhetoric and not on the business of combating terrorism.

"Sometimes the very idea of terrorism is used on right and left as politically convenient attack," Feingold said. "Rhetoric surrounding Sept. 11 seem to be everywhere … but the actual business of combating terrorism ... seems to be lost in the shuffle."

Bush seemed to presage Monday night's attacks on foreign soil in a tax-policy speech Monday in Omaha, Neb.

"There's still Al Qaeda operatives moving around," the president said.

"And we're going to stay on the hunt until we bring them to justice. We have a duty in this country to defend our freedoms. We have a responsibility to future generations of America to uphold our responsibility to make this country secure. And we assume those duties, and we accept that responsibility."

Fox News' Julie Asher and Wendell Goler and the Associated Press contributed to this report.