The American Federation of Government Employees, the largest federal employe union, said yesterday it has asked the AFL-CIO to put together a financial rescue package to keep the union afloat while it tries to organize new members.

AFGE President Kenneth T. Blaylock, in a statement issued by the union, said AFGE has "requested financial assistance from the AFL-CIO, and it has been offered." Blaylock insisted, however, that the union is "financially sound overall."

The AFGE is the bargaining representative for approximately 700,000 federal government workers, nearly 100,000 of them in the Washington-Baltimore area. AFGE also represents 6,000 employes of the District of Columbia. It runs a health-insurance program open to all federal workers and has been a major lobbying force on issues affecting federal employes -- from pay increases to a relaxation of the Hatch Act, which limits the participation of civil servants in politics.

Although AFGE bargains for 700,000 federal workers, only 207,000 belong to the union and pay dues. Over the last 15 years, AFGE has seen its membership cut nearly in half.

"We just don't have the kind of membership we used to," an AFGE official said. "No one ever thought it would get this bad under the Reagan administration. We're in a bind because our base has eroded."

The Blaylock aid request came amid reports that AFGE is so strapped for cash that it cannot continue operations for more than two or three months without outside financial aid. The union's National Executive Council has been meeting in Washington this week. The council yesterday was scheduled to take up next year's budget.

The National Treasury Employees Union, -- with 65,000 members, it is the second-largest federal union -- has launched a raid on AFGE's largest source of members, the Social Security Administration. The expensive battle to hang on to 63,000 of AFGE's current 177,000 active members (the rest are retired) is further draining union resources.

Labor sources outside AFGE said Blaylock requested financial help from the AFL-CIO about a month ago. Since then, AFL-CIO Secretary-Treasurer Thomas R. Donahue reportedly has won loan commitments from four unions: the American Federation of State, County and Municipal Employees (AFSCME), the Service Employees International Union, the National Association of Letter Carriers and the Communications Workers of America. All four unions have public employe members.

CWA President Morton Bahr, who has approximately 80,000 public employes in his 515,000 member union, said Donahue asked him about a month ago whether the CWA would be willing to participate in a loan package for AFGE. "Tom told me they were in a bind," Bahr said. An official from one of four other unions involved in the rescue plan called AFGE's cash flow "horrendous."

Bahr said Donahue did not mention any specific amount of money. An AFGE official said the amount of financial aid was "pretty much what Donahue comes back with." Donahue was unavailable for comment yesterday, but AFL-CIO officials have acknowledged the AFGE request.

None of the other three unions involved in the rescue plan would comment publicly about the situation. Privately, however, several union officials said they think AFGE will either have to begin showing substantial organizing gains or merge with another union. All four unions in the rescue plan have been mentioned as possible merger partners. The most logical union to take in AFGE would be AFSCME, the second-largest AFL-CIO union. It has 1.1 million members.

"We don't feel we're at that point," an AFGE official said when asked about a possible merger.

Blaylock's statement said, "While the union remains financially sound overall, the NEC (National Executive Council) has decided to realign the union's priorities and devote more resources to an already successful organizing campaign that is currently and consistently producing more than 3,200 new members per month."

An AFL-CIO official said the federation leadership was impressed enough with recent AFGE organizing efforts to put together a rescue package. He described any money from the AFL-CIO as "pump-priming for organizing."

Officials from other unions seemed less sure. "I don't think they can make it to their convention," said an official from one of four unions involved in the rescue package. The official, who requested anonymity, said any money from the AFL-CIO would be to try and allow AFGE to survive until its convention in August. Then, he said, it would be up to AFGE to raise money from its members.