Mayor Marion Barry, warning that the District of Columbia faced "disquieting new realities" of sharply reduced federal aid and growing joblessness and suffering, began his second term yesterday with a regal, day-long inaugural celebration that even Barry jokingly called a "coronation."

During an inaugural ceremony for Barry, City Council Chairman David A. Clarke and six other council members at the Washington Convention Center, Barry echoed the lament of mayors across the country that President Reagan's policies were strangling big cities and forcing them to impose drastic cuts in social services to make ends meet.

"The new reality makes plain a national policy to fund bullets over babies, to shelter missiles rather than the elderly and the homeless, to give a $750 billion tax break to the most wealthy, but to cut Medicaid, Medicare and Aid to Families with Dependent Children by over $17 billion," Barry said.

In foreshadowing an austere fiscal 1984 budget that he plans to unveil next week, Barry told the gathering of 2,500 supporters and city officials that "the choices we must make will be difficult; the path will not be smooth."

Barry promised to protect the very young, the very old and the handicapped from the severest of the program cutbacks, although he stressed that he was determined to find ways to get people off welfare and into jobs. Despite the city's dire budget straits, the mayor said he plans to boost spending for the criminal justice system in an effort to further reduce crime.

"I serve notice to the underbelly of our city that we will not rest until they are permanently removed as a blight on our landscape," the mayor said.

Police Chief Maurice T. Turner, who attended the ceremony, said that the city's crime rate dropped by 3.2 percent in 1982. He said his goal is to further reduce the crime rate by 8 percent in 1983.

"I'm very optimistic," Turner said. "We've put programs in place and we will reap the benefits of those."

Barry, 46, the son of Mississippi sharecroppers, rose to prominence in Washington as a community organizer, president of the school board and member of the City Council before he was elected to his first term as mayor in 1978. Yesterday he appeared cheerful and composed as he presided over a long day of inaugural ceremonies and hoopla that was diminished only by the sparse attendance along the route of an inaugural parade.

Barry, dressed conservatively in a blue three-piece suit, whisked around town on a bright, chilly day with his wife, Effi; their 2-year-old son, Christopher; Barry's mother, Mattie Cummings, who still works as a housekeeper in Memphis; and Barry's two sisters, Gloria Driver and Elizabeth Barry, both of Memphis.

"He's always been a good brother," Gloria Driver told a reporter. "We're definitely proud of him, particularly since this is his second time around."

Also inaugurated yesterday were council members Frank Smith Jr. (D-Ward 1), a school board member elected to Clarke's old seat; and incumbents Polly Shackleton (D-Ward 3), William R. Spaulding (D-Ward 5), Nadine P. Winter (D-Ward 6), Betty Ann Kane (D-At large) and Hilda Mason (Statehood-At large).

The inaugural events--including a large prayer breakfast, the parade, a swearing-in ceremony accompanied by the National Symphony Orchestra and a black-tie ball at the Convention Center--cost about $150,000 to produce.

The festivities were a far cry from the informal people's inaugural that Barry staged at the start of his first term in 1979. At one point yesterday, Barry quipped to reporters: "The coronation is going on."

Barry and his entourage rose early yesterday to join 2,300 supporters and friends at a $15-per-head prayer breakfast in the cavernous International Ballroom of the Washington Hilton.

Several of the mayor's key supporters, including Max N. Berry, an attorney and chairman of the Pennsylvania Avenue Development Corporation; attorney R. Robert Linowes; and John W. Hechinger, a businessman and D.C. Democratic National Committeeman, helped preside over the breakfast.

D.C. Del. Walter E. Fauntroy, who also took the oath yesterday for the start of another term in Congress, urged Barry and council members to begin an era of cooperation. "Let us not spend our time in office preparing to run for other offices," he said. "Let us do the jobs we were elected to do."

Wiley A. Branton, dean of the Howard University School of Law and a keynote speaker, said the District's problems have been made worse by the meddling of Congress--particularly its opposition to the enactment of a D.C. income tax on Virginia and Maryland residents who work in the District.

"The city has hundreds of bosses in the form of the U.S. Congress constantly giving conflicting orders on what we should do and how we should proceed," said Branton.

The inaugural parade, a colorful hodgepodge of high school marching bands, floats, trucks and long, sleek limousines, moved slowly along barricaded portions of downtown streets, past the District Building at 14th Street and Pennsylvania Avenue, and then on to the Convention Center. The Rev. David H. Eaton, president of the school board and Barry's pastor at All Souls Church, was the parade's grand marshal.

The sparse crowd along the 14-block parade route included Barry campaign workers, parents and relatives of high school band members, city workers and tourists. Some of them waved tiny red and white flags that were passed out by inaugural workers.

Rosemarie Rothmund and Peter Timm, two German tourists who arrived in Washington Sunday for a three-day visit, said they were on their way to the National Gallery when they ran into the parade at the corner of 14th Street and Constitution Avenue NW.

"We thought it was the swearing in of the senators. Is that correct?" asked Rothmund.

Larry Smith, a 32-year-old roofer from Northeast Washington who said he has been out of work for a year, watched the parade on Constitution Avenue near 10th Street on his way back from a job interview.

"I hope it the employment situation will be better under Barry, but it's hard to say," said Smith, who voted for Barry. "It seems like he tries to do what he can."

About a dozen demonstrators from the Community for Creative Non-Violence, who had camped in front of the District Building since last Tuesday to protest the shortage of emergency shelter for homeless people, were forced by police to temporarily move across the street during the parade. The group claims that four men died of exposure last month because the city hasn't made shelters easily accessible. One protester held up a placard that said, "Open shelters, not graves."