In a trade-off to hang onto labor's shaky support for his plan to overhaul the Civil Service system, President Carter yesterday approved a set of labor-management provisions that could greatly strengthen the position of federal employe unions.

In what administration officials termed a "significant move" to meet union desires, the president agreed to a system in which federal workers could chose between the regular government appeals system and union grievance and arbitration machinery in the case of firings and discrimination complaints.

A host of other employe disputes, over such matters as denial of raises, would be handled through the union grievance system.

The president also agreed to something the unions have fought for since 1962, but which five successive presidents of both political parties denied them: he proposed to take the federal labor management code out of the category of a presidential directive - which means that it could be altered or abolished at any time by the president and give it the "statue and stability of law."

Carter made another strong appeal yesterday for his civil service package in a press conference before the labor proposals were announced.Reemphasizing his personal commitment to meaningful changes in the current system, he said he would "object very strenuously" to any congressional efforts to weaken the proposals.

The president said also that he objects to "false accusations" about the plan, specifically the suggestion that it would "inject politics and possible abuse" into the system. He said his plan specifically removes the likelihood of such abuse.

In a letter to the chairmen of key House and Senate committees, James T. McIntyre Jr., director of the Office of Management and Budget, outlined the labor provisions and added that draft legislation containing them would be sent to Congress soon for inclusion in the president's civil service overhaul package.

The administration has also agreed to revise or clarify the language of more than half of the 23 passages in in the civil service bill to which union leaders had objected.

These passages deal primarily with employe rights, such as the right to a hearing, the burden of proof in an appeal, and whistle-blower protection.

A spokesman for the AFL-CIO-backed American Federation of Government Employees (AFGE) said yesterday the president's proposals mean "we've come an awful long way down the line" toward union goals. But, he added, "I can't say for sure this will be sufficient" to assure the union's active support for the entire civil service package.

Union representatives will comment formally on the president's move and their own position tomorrow when they testify before the Senate Governmental Affairs Committee, which has been conducting hearings on civil service reform, the spokesman said.

While other federal employe unions have actively opposed the president's civil service proposals, AFGE president Kenneth Blaylock has risked the wrath of his membership and other union leaders by dangling his support for the plan as bait for some administration concessions to labor, and particularly for AFGE, the largest and most powerful federal union.

Though the president's proposals yesterday did not go as far as the unions and their congressional backers would have liked, they were "certainly a step in the right direction," as one Capitol Hill source put it.

The president stopped short of giving the union leaders two things they were pressing for: a broader scope of bargaining, such as the right to bargain for pay, and a provision for some form of agency shop.