Several bomb threats -- which turned out to be groundless -- emptied schools and office buildings in the Washington area yesterday, as officials announced stricter security measures at buildings throughout the region while also seeking to quell the public's fears of terrorism.

But the sheer volume of them -- four to schools in Fairfax County, at least 10 to various sites in the District, two in Prince George's County -- and the quick response by bomb disposal teams underscored the apprehension about a possible terrorist attack in the Washington region in the wake of the opening air strikes on Iraq.

One official knowledgeable about security measures here this week said the FBI, which is leading counterterrorism planning from its local office in Southwest Washington, is taking some reports of terrorism extremely seriously.

"The feds are as serious as two heart attacks," the official said.

While an attack on a prominent government building would send a "terrific message," law enforcment agencies know of "no credible threat to the Washington area," said Thomas E. Duhadway, special agent in charge of the FBI's Washington field office.

Terrorism experts said that the public concern about terrorism far exceeds the danger.

"I get this feeling of a ground swell of hysteria that is sweeping across the country," said Arthur E. Gerringer, a director of the Institute for Strategic Studies on Terrorism, in Early, Tex.

"I think that is somewhat misplaced at this point," he said.

In the District, authorities have identified 15 to 20 sites that could be attractive to terrorists, including power, transportation and communications systems, as well as Jewish and Arab centers, the source said.

One concern is that terrorists could time an attack at rush hour, when rescue vehicles would be hampered by the region's notoriously congested traffic system.

Officials also fear that terrorists could blend into anti-war protests, using activists as "a shield or cannon fodder," the official said.

Some government officials, while acknowledging that Washington could be a choice target for terrorism, have tried assiduously in public statements to avoid overstating the threat. Security experts recommend understatement in times such as these, to avoid flogging emotions needlessly, and sending a message to adversaries that Americans are frightened.

Virginia Gov. L. Douglas Wilder said that several sites in the state, which is home to the world's largest naval base at Norfolk, have been threatened with terrorism. Wilder declined to name the sites or to provide other details, but police in Hopewell and Petersburg said that callers had threatened to blow up hospitals and the Hopewell police station Wednesday night.

"Government will be business as usual," D.C. Mayor Sharon Pratt Dixon said Wednesday night. "We will have a much more alert police force, but there is no need for fear . . . . We are more vulnerable than most other communities. However, we are more poised than most other communities to deal with security problems."

Her spokesman, Paul Costello, said yesterday that D.C. police have assigned added security at "all the vital channels, including water, transportation, power and travel," including bus and train stations, and the District Building.

In Annapolis, Gov. William Donald Schaefer told Marylanders to be on guard for possible terrorist activies and not to hesitate to report suspicious people or events.

"Prevention begins with the people," said Bishop L. Robinson, Maryland secretary of public safety and correction. "We will respond to your needs, real or imagined . . . . Call 911."

Police in Montgomery and Prince George's County met yesterday with directors of Jewish schools and rabbis at synogogues to discuss security precautions.

Private businesses also have stepped up security, in some cases sending instructions to their employees to watch for everything from new delivery personnel to unattended suitcases.

There have also been false alarms, which officials generally regard as pranks. An Army bomb squad was called to the Army Court of Appeals yesterday after someone spotted a package with Arabic writing on the wrapper. It contained a cassette.

Security officials at the Smithsonian Institution's Museum of Natural History closed its rotunda Wednesday and called in bomb-sniffing dogs and an Army bomb squad, after someone reporting seeing two men leave something in a locker and leave the building. Three hours later, after the bomb disposal unit determined that the locker contained nothing more than a coat, the two men, tourists from India, returned to retrieve it.

Simple logic, as several government officials said yesterday, dictates that the Washington area is a top target for terrorism, with its plethora of government officials and diplomats, embassies, defense contractors and military installations.

Some law enforcement officials say privately that they are more concerned about an attack on a shopping mall, restaurant or other gathering place than on a secure government building.

"There is the motivation for terrorists to bring the war home to the United States . . . to exact retribution," said Bruce Hoffman, a terrorism expert with the Rand Corp. "State-sponsored terrorists want to raise the stakes in the conflict through orchestrated, bloody attacks and use the violence to wear away at the public's resolve to support . . . continued military presence in the gulf."