Real after-tax income for the average American rose 6.8 percent last year, an increase in purchasing power matched only once in the last 20 years, the Commerce Department reported yesterday.

The sharp increase in real after-tax income was attributed to strong growth in employment, moderate inflation and the tax cut in 1983.

Real personal disposable income increased 3.5 percent in 1983 and 0.5 percent in 1982, during the recession. In 1973, it also grew by 6.8 percent and increased by 7.1 percent in 1964.

Personal income, unadjusted for inflation and taxes, also moved strongly in November and December, in line with other government statistics that suggest the economy may be rebounding. Personal income rose 0.5 percent in December and 0.6 percent in November, Commerce said.

White House spokesman Larry Speakes said the personal income report "generally supports a view that the economy has strengthened in both November and December." He said the statistics suggest "considerable promise for 1985."

Most of the improvement in personal income came in the beginning of the year, when employment gains were strong and inflation remained low, said Robert Ortner, the chief economist for the Commerce Department. However, increases in personal income accelerated slightly at the end of last year, which bodes well for a rebound in consumer spending, after a slump this summer and fall and moderate acceleration in economic activity.

"The key is inflation hasn't picked up at all in 1984," Ortner said. Income this year should grow well, but growth should not be as strong as it was in 1984, he said.

Inflation, measured by the implicit price deflator for personal consumption expenditures, was 3.2 percent in 1984, compared with 3.7 percent for 1983.

Economists said that household spending will probably be sluggish until the middle of 1985 despite the increases in personal inome and high consumer confidence, in part because household debt is still high. According to Data Resources Inc., household debt as a share of disposable income was 10.3 percent at the end of last year, down from its early summer high of 10.6 percent.

In December, personal consumption spending increased 1.2 percent, following a 1.0 percent rise in November and decline of 0.4 percent in October.

Wages and salaries rose $18.3 billion in December, compared with $13.8 billion in November. Payrolls of commodity-producing industries rose $6.7 billion, compared with $3.6 billion in November. Payrolls in services rose $6.3 billion in December, compared with $4.2 billion the previous month.

For 1984, personal outlays rose 9.0 percent, compared with 8.7 percent the previous year, Commerce said.

Personal saving -- disposable personal income less outlays -- rose 32.9 percent, following a drop of 13.2 percent in 1983, Commerce said.

The implicit price deflator -- a measure of inflation -- increased 0.1 percent in November, following a 0.3 percent increase in October. An inflation figure was not available for December.