The United States, however, is not raising its terror alert status,
CBS News correspondent Bob Orr reports officials across the U.S. government continue to say they see no intelligence indicating any imminent attack against America, and no evidence so far linking the U.K. attacks to any wider plot involving the U.S.
"There is no indication of any specific or credible threat to the United States — no change in the overall security level," White House spokesperson Tony Snow told reporters in Maine.
A spokesman for the FBI says agents remain in constant contact with British law enforcement authorities, and are "waiting to see if there are any U.S.-based investigative leads to pursue."
Britain raised its security alert to the highest level possible, an indication that terrorist attacks are imminent.
Snow said after this step was announced in London that the British government had notified the White House in advance, and that it did not provoke any change in the threat assessment in the United States. "We constantly monitor and assess the situation, and adjust our posture as necessary," he said.
Still, U.S. officials were wary. Acting out of "an abundance of caution" during the upcoming Fourth of July holidays, Homeland Security chief Michael Chertoff said the government is putting in place plans to increase security at airports, on mass transit and at transportation facilities.
"Some of these measures will be visible; others will not," he said in a statement.
Chertoff added that "at this point, I have seen no specific, credible information suggesting that this latest incident is connected to a threat to the homeland. We have no plans at this time to change the national threat level, although we remind everyone that the aviation threat level has been raised to orange since last fall."
Orange is No. 2 of five levels and indicates a high risk of terrorist attacks. The current national threat level is yellow, or the third highest, indicating an elevated threat.
The Transportation Security Administration is posting more agents outside terminals at some airports, Snow said.
But, terrorism experts said that events in London are reasons to be concerned.
"We have to assume that this is a pattern, and we are going to see more of the same thing," said CBS News terrorism analyst Paul Kurtz. "Not only in England, but elsewhere in Europe and the U.S."
Travelers across the U.S. were already talking about the Glasgow attack on Sunday, but most said they would spend this July Fourth showing their independence from fear, reports CBS News correspondent Joie Chen.
"There will be some inconvenience of passengers in terms of longer wait times," Snow said. Local police also may take separate measures, he added.
"The most you're going to see right now is some inconvenience — some increased inconvenience of airline passengers, more likely at large airports than small," Snow said.
Police stepped up curbside patrols with canine units at Hartsfield-Jackson Atlanta International Airport. The Port Authority of New York and New Jersey, which operates Newark Liberty in New Jersey and John F. Kennedy and LaGuardia airports in New York, took "a number of measures as we always do to respond to security situations immediately," spokesman Steve Coleman said.
Operations at Miami International Airport went on heightened alert through at least Independence Day. Officials were increasing patrols around the perimeter of Philadelphia International Airport.
"Certainly there is a high awareness," said spokeswoman Carolyn Fennell at Orlando International Airport in Florida. "We have taken steps in due diligence and are applying measures that are already in place."
At Washington's Reagan National and Dulles International airports, spokesman Ron Yingling said some measures are behind the scenes. "I don't think there's anything different in what passengers have to physically do to get through security that's different from yesterday."
Bush, who spent the day biking and fishing, was kept abreast of the developments in Britain, Snow said. U.S. officials were in contact with their counterparts in Europe, Snow said.
Chertoff said his department and the FBI have provided updated and guidance on protective measures to state and local homeland security and law enforcement agencies.
FBI spokesman Richard Kolko said the bureau stood ready to help British authorities.
Two men rammed a flaming sport utility vehicle into the main terminal of the airport in Glasgow, Scotland, crashing into the glass doors at the entrance and causing a fire, witnesses said. Police said two suspects were arrested.
The airport — Scotland's largest — was evacuated and all flights suspended. Hours later, Britain raised its security alert to "critical."
On Friday, British police thwarted a plot to bomb central London, discovering two cars abandoned with loads of gasoline, gas canisters and nails. Detectives said they were keeping an open mind about the suspects in the London case.
Bush was in Maine to host Russian President Vladimir Putin at the Bush family's summer home on the coast. Putin was to arrive Sunday for a two-day stay.