Mayor Marion Barry formally began his reelection campaign yesterday, pledging to about 700 supporters that he is committed to cracking down on street crime and assuring the many city employes sitting in the audience that there will be no further layoffs if he wins a second term.

Barry, who already has attracted a large field of eight opponents in the Sept. 14 Democratic primary, admitted he has made mistakes during his 3 1/2 years as mayor but stressed that he now understands the city government better than any of his challengers and he is better equipped to be mayor.

"The road has not been easy," said Barry, who was accompanied by his wife, Effi, his 21 month old son, Marion Christopher, and his mother at the rally at the Ann Beers Elementary School near Barry's Southeast Washington home. "We've made mistakes. We've learned from those mistakes. Although we've not done all that we wanted to do, we've laid the foundation for fulfilling our commitments and achieving our goals.

"As citizens," he added, "we understand the urgency of the time, we understand the urgency of the hour. We understand the need for strong and compassionate leadership. . . My adminstration has set a standard for this type of leadership."

The mayor's tough rhetoric about clamping down on crime, particularly drug dealing, came as no surprise after his announcement Thursday that he would put 242 more police officers on the streets by May and use more than six dozen squads armed with shotguns to stake out frequently-robbed businesses.

But Barry appeared to have startled his own top aides by flatly promising that there would be no additional layoffs of city workers during the next four years--a pledge apparently aimed at city labor groups who suffered heavy losses during Barry's first two years in office as he tried to reduce city spending to cope with a budget deficit.

"I'm not going to RIF one soul in '82, 83, '84, '85, or '86," Barry declared, drawing loud applause and cheers from the audience, many of whom were government workers.

"I can see my budget officer is having a heart attack," he added, looking at budget director Gladys Mack who was seated in the front row of the audience. "She's saying: 'Mr. Mayor, where are you going to get all that money from?'"

Later city administrator Elijah B. Rogers, who led a group of about 40 of the mayor's top aides and department heads to the campaign kick-off, said it would be difficult to keep the pledge but added that the city's economy will probably be strong enough to sustain the city's budgets without requiring further cutbacks in personnel.

"It will be difficult," Rogers said, "but we'll do it. The mayor has made a pledge and it's Gladys Mack's and my responsiblity to implement it."

Barry's speech came after a motorcade of more than 20 cars, many with the low-number license tags that the mayor and some other city officials distribute to supporters, drove from 7th and D streets NW to the public school auditorium with ribbons streaming.

The small school was filled to overflowing with a crowd that included many long-time Barry supporters, some wearing buttons from his previous campaigns and carrying blue and white balloons. Each of the city's eight wards was represented, according to Anita Bonds, the assistant campaign manager who worked as the head of Barry's constituent services unit in the city governemnt until she resigned a week ago to take charge of the campaign. Barry and Bonds met with several dozen key organizers Monday night to kick off the effort to bring together yesterday's rally crowd, an early test of Barry's campaign organization.

When Barry appeared, ushered in by Ivanhoe Donaldson, his campaign manager in 1978, he was given a standing ovation. Donaldson, now head of the city's department of Employment Services, plans to leave the government in May to head Barry's campaign.

After enthusiastic endorsements from speakers ranging from businessman John Hechinger, who is the city's Democratic national committeeman, to several ministers, Barry described his administration's accomplishments in managing city finances, improving the public schools, reducing crime, caring for public housing and maintaining programs for the elderly.

He also took a swipe at two of his opponents, city council members John Wilson and John Ray, both of whom have relied on political advertising early in the campaign.

"When the voters ask you what has Mayor Barry done after they have heard the catchy jingles and slick TV ads, tell them you won't find the mayor's accomplishments in a jingle," Barry told the crowd at the elementary school, which is about a block from his home.

Barry emphasized his administration's record in fighting crime, creating jobs, and housing.

He contended his administration is winning the war on crime although the rate of major crimes has gone up in the past three years. "The streets are safer now than they were this time last year, and they are going to be safer tomorrow," he said, "As long as I am mayor we are not going to be locked in our homes in fear of criminals."

While blaming President Reagan for policies that have hurt the city's economy, Barry said his administration has laid the foundation for 30,000 new jobs that will come with the convention center and other construction projects in the District.

Barry said he has created 21,200 summer jobs for young people. His administration was severely criticized for mismanagement of the summer jobs program during his first two years in office, when many young people went unpaid because of problems processing paychecks, but last summer the program ran smoothly.

"We are not going to be satisfied," Barry said, "until we try to find a job for each and every person in this city who wants to work."

The mayor said in an interview Friday that his relationship with businessmen in the city set him apart from other candidates because he can persuade the businessmen to create jobs here.

Barry said his administration has renovated or built 4,000 housing units "already standing, with people in them." And he said another 3,000 housing units are being prepared now.

In addition to making his record known, Barry in recent weeks has begun to take steps to head off criticism of his bureaucracy. He ordered a major effort to fix the city's troubled water billing system; started an anticrime program and requested supplemental appropriations for filling potholes.

He also asked that the city's Department of Transportation stay open extra hours this week to accommodate motorists who have not yet renewed their licenses.

In an interview Friday, Barry said he was taking those steps because the knowledge he has gained of the city government has enabled him to anticipate when problems will occur. At the same time, he said he wants to improve the image of his administration.

"It's not my weakness," Barry said in the interview, "but there is the perception among some people that the government doesn't work well. So whenever something happens that demonstrates that, whether it's the board of elections, which I have no operational control over. . . or when another agency I don't have any control over, the school system, doesn't deliver textbooks on time to teachers. . . there's the perception among people that the government doesn't work well and they attribute it to me."

Yesterday Barry did not mention any of his opponents by name, but several of his supporters who spoke indirectly criticized former Carter administration cabinet member Patricia Roberts Harris. Early polls have shown Harris running neck and neck with Barry for the nomination.

Barry indicated Friday that his campaign will emphasize his long personal involvement with the city.

"I have some qualities that are unique in the mayor's office," he said. "One, I really care about people. Whether I have the title of mayor or not, in the 20 years or so since 1960 and the civil rights movement, all through Free D.C. Movement, all through Pride a self-help organization he helped found in 1968 , onto the school board, and then the city council, it has been one constant demonstration of caring. . ."

Barry, 46, served on the D.C. school board from 1971 to 1974, when he was elected to the council.

Despite the fact that he begins the race as the incumbent, with strong financial support, early polls show Barry's strength among voters at or just below its level in 1978, when he ran as a challenger. He said in the interview that he believes he has both gained and lost supporters during his term, "depending on who you're talking to."

"I have picked up a tremendous amount of support from people who voted for former mayor Walter Washington. . . I've picked up not as much but significant support from people who supported Sterling Tucker in 1978," he said. "Now among those who supported me there has been some slippage but the slippage is not that major and primarily in some parts of Georgetown. . . Dupont Circle. . . Adams Morgan.

"My goal, as you well know, I tell everybody, is 52 to 55 percent of the vote," he added. "On the other hand if I don't get it and win the election, I'll still be the mayor."