Mayor Abraham D. Beame today declared his candidacy for re-election, raising to six the field of serious contenders in New York's quadrennial political bloodletting - the September Democratic mayoral primary.

Rejecting suggestions that at 71 he is too old and tired to grapple with the seemingly insoluble problems of the nation's largest city, Beame declared, "It is clear that we have weathered the storm, whose clouds have been gathering for more than a decade." He added, "I want to finish the job, and I'm the only one who can do it."

Beame sounded a theme that is likely to become central to his campaign, blaming former Mayor John V. Lindsay for New York's fiscal dilemma and saying that he inherited a $1.2 billion deficit from Lindsaay in 1973.

His opponents already have sacrastically sugested that if Beame is elected to a second term, he will indeed complete what he started, and will topple New York over the brink of insolvency.

Asked if he had a message for Gov. Hugh L. Carey, who abondoned Beame in a fractious political dispute in favour of the mayoral candidacy fo New York Secretary of State Mario Cuomo, Beame retorted, "Here I am, boys." He added, "I'm going to take 'em all on."

Already, five Democratic candidates of closely related political persuasions and constituencies have begun to pursue the job that Fiorello H. LaGuardia romanticized in the 1930s and which Lindsay 30 years later called the "most impossible" political office in America.

Although still formally unannounced, former U.S. Rep. Bella Abzug may be Beame's most imposing Democratic challenger, although she could splinter the liberal Democratic vote and wreak havoc among other contenders while emerging with less that the 40 per cent needed for nomination without a run-off election.

Abzug, who last year lost a Democratic Senate primary race to Daniel P. Mornihan after having given up her house seat for the opportunity, has said she will announce her candidacy next week. She has already been running hard, however, and last week won the endoresment of the New Democratic Coalition, the reform wing of the party.

Two other insurgents pose equally serious threats to Beame, partly because of their own broad-based supprot and partly because they have hired two of the most effective media wizards in the business.

Cuomo, a relatively unknown Queens lawyer who unsuccessfully ran for lieutenant governor in 1974, has signed up Gerald Rafshoon, President Carter's advertising man, who political observers say will probably package Cuomo as the quintessential problem solver.

Cuomo, a charismatic former professional baseball player and a close ally of Carey, got fleeting citywide fame in 1972 by saying the homes of 69 Italo-American families in Corona, Queens, which were threatened by a controversial urban renewal project. Later, he defused a potentially explosive black-white confrontation over public housing in Forest Hills, and more recently he meditated a volatile Indian land claim dispute after an armed band of Mohawks seized state parkland in the Adirondaks.

Rafshoon will find himself up against David Garth, the talented media adviser who three years ago helped propel Carey from a relatively obscure Brooklyn congressional seat into the statehouse in Albany.

Garth has been retained by U.S. Rep. Edward Koch, a mayoral candidate who dropped out of the 1973 race because of a shortage of funds. Kock, already is trying to raise enough money for an early television advertising campaign that strategists say will emphasize the candidate's reputation as an effective congressman and will try to overcome the heavy resistance liberal Democrats meet in Queens, parts of Brooklyn, Staten Island an other more conservative acres of the city.

Also announced is Manhattan Brough President Percy Sutton, the only black candidate, who is widely respected by professional politicians for his skill as a campaigner but who is regarded as a longshot.

The sixth candidate is Joel Harnett, periodical publisher and radio station owner who has said that he will run as an independent if he loses the primary.

U.S. Rep. Herman Badillo, who lost a 1973 primary runoff with Beame, and U.S. Rep. Mario Biaggi, who also unsuccessfully ran for mayor in 1973, are other contenders who have not announced but whose candidacies would be taken seriously by the local political professionals if declared.

As in all New York mayoral primaries, the lure of a $60,000-a-year salary and a house in about the only landscaped estate left in congested East Side Manhattan has attracted several fringe candidates who are not taken seriously by the politicians.

Leading that field this year is Louis Wein, who was fired from the Mayor's Task Force for Emergency Preparedness after sounding the alarm that city faced disaster because it was not prepared for earthquakes.

Apart from the hazards of a crowded ballot, Beame's greatest liability seems to be opposition by the powerful municipal labor unions - a legacy of his cutting the city payroll by 60,000 workers - and a frigmentation of support by the regular Democratic organization because of his abandonment by Carey and by Bronx Borough President Robert Abrams.

In what could be the most important mayoral election in New York history - in terms of fiscal survival - Beame is veiwed by many party strategists as vulnerable also because of the widespread notion that the city has lost control of its own government.

At the height of the default crisis, the legislature created an emergency financial control board to manage the city's pursestrings. That action passed some of the mayor's authority to the governor.

Moreover, Beame will have to answer charges that the quality of life in New York has deterioted rapidly during his first term - largely because of the fiscal problems.

However, Beame has assembled a skilled campaign organization that includes as manager Iim Hanan, a Mobil Oil executive who worked in the campaigns of John and Robert Kennedy. Hanan said the campaign woudl cost roughly $1.7 million, the same amount Beame spent in his successful 1973 race.