Anti-Castro Cubans, whose violent protests have previously centered largely in the Miami area, claimed responsibility for yesterday morning's two bomb explosions here near the White House and outside Soviet offices near 16th and L Streets NW.

The blasts heightened concern among security officials as leaders of 18 Latin American nations gathered in Washington to mark the signing of the new Panama Canal treaties. The explosions occurred only six days after Cuba opened its first diplomatic office here in 17 years.

One bomb exploded about 3 a.m. in a large concrete flower pot on a traffic island on E Street NW, only a short distance southwest of the White House. The traffic island separates the Ellipse from the White House grounds. No one was reported injured in either of the two predawn explosions.

The White House, disputing a report from a reliable investigative source, said that President Carter was not awakened by the blast. Press aides said the President would have no comment on the incidents.

Later, the Soviet Embassy's deputy chief of mission, Vladillen M. Vasev, lodged a protest with Assistant Secretary of State for European Affairs George Vest because of damage to Soviet offices caused by the first explosion.

The first bomb blew up at about 2:40 a.m. in a driveway behind a building at 16th and L Streets NW that houses ground-floor offices of the Soviet Embassy's maritime attaches and the Soviet airline Aeroflot.

The explosion was reported to have knocked out 52 windows in the building, including those of the Soviet maritime offices. It also destroyed windows in 37 rooms at The Capital Hilton (formerly the Statler Hilton Hotel), in most of which guests were asleep, and blew out windows in other nearby buildings, including 43 at The Washington Post, at 15th and L Streets NW.

Rightist Cuban refugee groups opposed to the regime of Prime Minister Fidel Castro claimed responsibility for the explosions in telephone calls to United Press International here and in Miami.

A male caller, speaking rapidly with a Spanish accent, reached Robert Shepard an overnight desk man for the news agency here, at 2:55 a.m., shortly after the first explosion, but minutes before the blast near the White House. The caller, Shepard recalled in an interview, told him his group had "just bombed Aeroflot" and had also placed bombs near the White House. About five minutes later, Shepard heard what was apparently the second explosion, several blocks from his office.

Shepard said the telephone caller identified his group as what sounded like the Pedro Luis Boitel commandos. The caller, he said, criticized Soviet support for Castro's regime, alleged human rights violations in Cuba, and use of Cuban military forces in Africa.

The group, named for a Cuban student leader who died in a Havana prison in 1972 during a hunger strike, surfaced May 25 when it claimed credit for an explosion at the Mackey International Airlines office in Fort Lauderdale, Fla. The small airline, which had planned to become the first domestic carrier to resume flights to Cuba, immediately dropped its plans. The group has also claimed responsibility for carrying out other bombings in Florida.

The second anonymous call to UPI yesterday was received at the news agency's Miami office shortly after 6 a.m. The Miami bureau is closed from 1 a.m. to 6 a.m., and Les Kjos, a UPI reporter, said a phone was ringing when he arrived for work.

A man with a slight Latin accent told him, "Listen carefully. The bomb that went off in Washington today was put by the Cuban anti-Communist commando El Condo in retaliation for giving away to the Communists the Panama Canal. Goodbye." Then, Kjos said, the caller hung up.

El Condor is a rightist Cuban splinter group that has claimed credit for several bomb explosions in the Miami area. Kjos noted that an anonymous caller had told UPI last week that the Boitel commandos and El Condor had merged. Panama's military regime has long been denounced by rightist opponents as Communist and by leftist critics as a repressive dictatorship.

FBI officials have been concerned recently over the possibility of violent protests here by anti-Castro Cubans because of warming U.S. relations with the Castro government. The diplomatic office opened here by Cuba last week - in the latest sign of growing U.S. Cuban links - is known as an "interest section." Eight Cuban members of the interest section are now housed here at the Czechoslovakian Embassy.

Although anti-Castro Cubans are suspected, according to informed sources, in the bombing death here last Sept. 21 of former Chilean Foreign Minister Orlando Letelier, no organization has claimed repsonsibility for the killing.

Yesterday's bomb explosions set off investigations by the FBI and other federal and local law enforcement agencies. A rash of bomb scares occurred later in the day, prompting the evacuation of numerous buildings. Traffic tie-ups also resulted, as police cordoned off streets near the sites of the two explosions.

The bombings occurred amid elaborate security preparations surrounding the signing here of the Panama Canal treaties. Spokesmen for the Secret Service and the State Department's security office termed these their largest security operations in Washington since President John F. Kennedy's funeral in 1963.

Despite the enormous security precautions, yesterday's explosions were detonated at sites to which public access is largely unrestricted. According to reliable investigative sources, a Soviet guard, normally on duty inside the building damaged by the first explosion, was not present at the time. The traffic island near the White House, where the second blast occurred, is in an area patrolled during predawn hours only by one foot patrolman and one squad car, according to a U.S. Park Police spokesman.

Even though the blast near the White House was clearly audible several blocks away, it took investigators two hours, according to reliable sources, to locate the flower pot on the traffic island where the bomb went off. The only damage apparently caused by the explosion was to the think, 300-pound flower pot - one of 15 in the traffic island - and to the geraniums it contained. The damage was estimated at $145, a spokesman said.

Conflicting reports emerged yesterday about the nature of the two bomos.

According to reliable investigative sources, the bomb that exploded near the Soviet offices was composed of a modern military substance, a plastic known as C-3 or C-4. The bomb detonated near the White House was suspected of being made of the same substance, according to these sources.

This report differed from earlier accounts given by other investigators. George Berklacy, a spokesman for the U.S. Park Police, said the device set off near the White House was initially believed to be a pipe bomb filled with gunpowder. The bomb planted near the Soviet offices had initially been reported to be dynamite.

The blast near the White House was triggered by a timing device, according to several investigative officials. There was no apparent conflict over this point, and investigators said fragments of the timing device were found at the site. It was not known yesterday how the bomb near the Soviet offices was detonated.

FBI officials said they would investigate possible smilarities between the bombs planted here and those set off in Florida apparently by the Boitel group.

According to reliable sources, the explosions were powerful enough to have killed anyone within 20 feet. The blasts also sent glass fragments flying at an estimated 1,000 feet per second. Had anyone been strolling along L Street between 15th and 16th Streets when the explosion occurred, such a person would likely have been knocked down by the blast, investigators said.

The explosion near 16th and L Streets NW set off crosscurrents that knocked out windows on both sides of the street. Investigators said that some windows were smashed by the initial impact of the blast, while others were sucked out by a vacuum created in the explosion's wake.

At the Capitol Hilton, guests who were asleep in their rooms apparently escaped injury partly because the vacuum created by the blast pulled their windows into the street, rather than hurling glass into their rooms. Other nearby buildings damaged by the explosion either were vacant or had only small staffs on duty in the early morning hours. Offices oon the L Street side of The Post building were not staffed at the hour when the explosion occurred.

Thomas French, a mortgage banker from Alvin, Tex., and his wife, Nona, were asleep in their room at the Capital Hilton when the bomb exploded. "We weren't aware our window was blown out at first," French said in an interview later in the day as he sat in his hotel room. It's main window was missing and glass shares littered the sill. He noted that the blinds had been nearly closed and a curtain had apparently deflected glass blown into the room. "As it turned out, we were not hurt," he added.