President Carter, stepping up his campaign for an overhaul of the government's much-criticized civil service system, sought to assure federal employes last night that his sweeping proposals would not endanger their jobs.

In a round-table discussion in the cafeteria of Fairfax High School, the president asserted that there is "no way" his legislative proposals for revamping the civil service system "can possibly hurt any competent and dedicated public servant."

At the same time, Carter left no doubt that he intended to tighten disciplinary procedures, including the possible firing of government employes. While noting that his plans were designed to reward excellence and to protect so-called "whistle-blowers" who expose problems or wrongdoing, he also said he wanted to "single out those who were incompetent or lazy or not dedicated" and subject them to stern disciplinary measures.

Carter took his campaign for broad changes in the deeply entrenched civil service system to Fairfax City at a time when his proposals face major congressional tests and strong opposition among many federal workers, their unions and supporters in Congress.

The House is expected to begin floor action within the next few weeks on a sharply modified version of Carter's proposals. The Senate considerations appear to face greater uncertainties, with some sources predicting a possible filibuster.

In the relatively informal atmosphere of the suburban high school, Carter fielded questions from eight Virginia residents, ranging from low-and high-ranking federal employes to a Republican lawyer and a union accountant.

The president was flanked at the table by Alan K. Campbell, the Civil Service Commission's chairman who has been Carter's point man in his drive for civil service changes, and by Rep. Joseph L. Fisher (D-Va.), who represents the Fairfax district and who has avoided active opposition to Carter's plans.

The first question of the one-hour session, which was televised in the Washington area and aimed at gathering nationwide media coverage, was asked by Dwight F. Rettie, an Arlington resident and National Park administrator. Rettie, who has previsously been critical of some parts of Carter's civil service legislation, said he was "deeply troubled" by the president's plan to offer cash bonuses for government workers as a reward for competence. Rettie argued that these would be "basically at odds with the concept of public service."

Carter replied, "I've chosen a career of public service myself." Then he went on to contend that his proposals offered rewards for skilled government employes tht included responsibility, rather than solely higher pay.

"It is not just a matter of increased financial rewards," Carter said.

Although one panelist pointed out that Carter's questioners had not been briefed or coached in advance, none of the panel members asked hostile or bitter questions. Several in fact, stressed that they supported at least some parts of Carter's civil service package.

All day long, the small suburban Fairfax City community had prepared for the president's visit. Workmen trimmed bushes, cut grass, picked up trash and scrubbed walls, windows and doors at the sprawling, brick Fairfax High School City Police Chief Larry F. Wines announced that virtually the entire 47-member police force had been put on duty last night.

"It's a big honor," said a worker who was on his knees, scrubbing the bottom of one of the school's front doors.

There had been a frantic scramble for the 400 tickets that were parceled out by civic organizations to Virginians who wanted to be in the high school audience. Barbara Weiss, a government employe's wife, was jubliant yesterday when she finally got a ticket after three days of futile pleas. "I'm going home to blow dry my hair," she said.

Fairfax City Mayor Frederick W. Silverthorne put on what he described as "my going-to-prayer-meeting clothes" - a brown plaid two piece suit - to greet the president. Carter arrived by helicopter on the school's empty soccer field and was welcomed by a 12-second ovation as he entered the school cafeteria, where the roundtable discussion took place.

The president's trip to the suburbs also sparked some dissent. Some members of the National Treasury Employee's Union, which has opposed Carter's civil service proposals, picketed outside the school.

Carter's appearance last night was the latest in the administration's drive to win public and political backing for overhauling the civil service system - a campaign that has been under way for more than a year. Carter sent his legislative proposals to Congress March 2, asserting that "civil service reform will be the centerpiece of government reorganization during my term in office."

Since then, the Carter administration's civil service plans have taken a beating from members of Congress, labor unions representing federal employes, veterans' groups and others. Widely divergent measures have emerged from key House and Senate committees. Both bills differ significantly from Carter's initial recommendations, leaving prospects for eventual enactment far from clear.

The House Post Office and Civil Service Committee has reversed the thrust of Carter's proposals in an attempt to give federal workers and their unions increased leverage and broader job proections. The committee's bill also includes a hotly disputed provisions allowing federal workers to engage in partisan poltical activities that are currently barred by the Hatch Act.

The Senate Governmental Affairs Committee's bill more nearly resembles Carter's plan, but the committee rejected a controveersial Carter proposal that would curtail the longstanding system of preferential hiring and job-retention treatment for military veterans who weren't disabled.

Although the largest federal employes' unions were initially split over Carter's civil service plans, they have now all lined up in support of the House committee's version. Business groups have backed Carter's civil service proposals and vehemently oppose the House committee measure.

Among key elements in the Carter administration's package were stream-lined hiring and firing procedures, a new coarrot-and-stick system of pay incentives an elite corps of senior executive who would trade some job security for a chance at higher pay for superior performance and a pledge to give unions greater collective bargaining rights.

A separate administration-proposed reorganization plan for splitting the Civil Service Commission into two agencies - one to handle personnel management and another to examine grievances and alleged abuses - will go into effect next Friday unless it is vetoed by either house of Congress by then.

Carter's use of the question-and-answer format last night fit in nearly with recent efforts by White House aides, including media adviser Gerald Rafshoon to improve the president's public image. The contend that Carter does well at fielding questions from the public. They also believe he must hammer repeatedly on an issue to gain support for the administration's view.

In the past few days, Carter and other administration officials have repeatedly pushed for their civil service proposals. Carter talked about them Tuesday with a group of businessmen. A White House position paper on civil service reform was also issued this week.

By going to Fairfax High School, Carter placed himself not only in an area where many federal employes live but in a congressional district where his civil service proposals appear to have gathered at lest limited support. Fisher, virtually alone among the Washington area congressional representatives has avoided any active oppostion to Carter's civil service plans, although Fisher has expressed some reservations about them.