Last Updated 11:35 a.m. ET
Homeland Security Secretary Janet Napolitano said the government has no plans to raise the terror alert level in the U.S. as a result of Osama bin Laden's death.
Napolitano said elevated terror alerts will only be issued when the government has specific or credible intelligence it can share with the American public.
She also said the country remains at a heightened state of vigilance, and that the U.S. is safer than it was on September 11, 2001 because bin Laden is dead.
CBS News Homeland Security correspondent Bob Orr said this morning on "The Early Show" that the terror threat level is not being raised in the traditional sense - there are no color-coded terror threat levels any more - but that "significant portions of the U.S. government and military installations, and law enforcement agencies are kind of raising their guard."
U.S. security and intelligence agencies have ramped up their surveillance and been told to look for any attack plans which could be accelerated.
Orr says the FBI has issued a warning against possible retaliatory strikes from al Qaeda and sympathizers and asking people to be on the lookout for any signs or evidence of something in the works.
"As far as we know, there is no credible threat out there - nothing in the pipeline, so to speak, but it is true that America is on guard," Orr said.
Some local law enforcement agencies in the U.S. are adding security measures following Osama bin Laden's death, out of what one called "an abundance of caution."
The Port Authority of New York and New Jersey says it will add more police Monday at airports, bridges and the World Trade Center site itself. The NYPD has increased police patrols on the city's subways this morning out of an abundance of caution, according to a statement issued by Deputy Commissioner Paul Browne.
In Los Angeles, police say they're stepping up intelligence monitoring.
The agency says the extra police is not a response to any current threat "but out of an abundance of caution until we have the chance to learn more" and that the facilities it runs will operate normally otherwise.
And a lieutenant says police in Philadelphia were on heightened alert, checking on mosques and synagogues every hour.
Orr said the threat of retaliation against bin Laden's death is a major concern.
"I don't know that that would be today or tomorrow," Orr said. "They tend to think longer-term. They're strategic planners. We could face a sizable risk down the road. The one thing that's kind of a wild card in this is, because al Qaeda has fractionalized and splintered, the base of operations - the real power base - has kind of shifted to Yemen and al Qaeda in the Arabian Peninsula (AQAP). It could be that the leader of AQAP there, and the American-born radical cleric Anwar al-Awlaki."
[It was al Qaeda's Yemen branch that almost took down a U.S.-bound airliner on Christmas 2009, and nearly detonated explosives aboard two U.S. cargo planes last fall.]
Orr said there is also the risk of the so-called lone wolf - "Someone, perhaps even living in this country, that could view the killing of bin Laden as unjust and take something into their own hands, try to strike out."
The State Department early Monday put U.S. embassies on alert and warned of the heightened possibility for anti-American violence around the world.
In a worldwide travel alert released shortly after President Obama announced bin Laden's death, the department said there was an "enhanced potential for anti-American violence given recent counterterrorism activity in Pakistan."
"Given the uncertainty and volatility of the current situation, U.S. citizens in areas where recent events could cause anti-American violence are strongly urged to limit their travel outside of their homes and hotels and avoid mass gatherings and demonstrations," it said.
The alert said U.S. embassy operations would continue "to the extent possible under the constraints of any evolving security situation." It noted that embassies and consulates may temporarily close or suspend public services, depending on conditions.
Meanwhile, a jubilant crowd gathered outside the White House as word spread of bin Laden's death after a global manhunt that lasted nearly a decade.
President Obama gave a live news conference from the White House just before midnight Eastern to confirm bin Laden had been killed in a U.S. operation, saying, "Justice has been done."
The development comes just months before the 10th anniversary of the Sept. 11 attacks on the World Trade Centers and Pentagon, orchestrated by bin Laden's al Qaeda organization, which killed more than 3,000 people.
The attacks set off a chain of events that led the United States into wars in Afghanistan, and then Iraq, and America's entire intelligence apparatus was overhauled to counter the threat of more terror attacks at home.
Al Qaeda was also blamed for the 1998 bombings of two U.S. embassies in Africa that killed 231 people and the 2000 attack on the USS Cole that killed 17 American sailors in Yemen, as well as countless other plots, some successful and some foiled.