Corporate profits soared last quarter at an exceptionally fast pace, evidence of excess demand in the economy that pushed production to near capacity and intensified inflationary pressures.

Commerce Department figures showed yesterday that before-tax profits rose 9.7 percent in the final three months of 1978, an annual rate of 44.8 percent. Over the whole year, profits rose 26.4 percent.

At the same time, the department revised its estimate of the economy's growth during that quarter to a rapid 6.9 percent, almost a full percentage point higher than first reported.

The corporate profits figures present a political embarrassment to the Carter administration, which is trying to persuade organized labor to stay within voluntary wage guidelines in the face of sharp price increases.

Trying to head off criticism that the wage-price program penalizes workers while letting businesses reap extralarge profits, presidential inflation fighter Alfred E. Kahn emphasized that "high profits are not bad and do not necessarily mean that a company is not in compliance with the guidelines."

But Kahn conceded that the profits boost "will strengthen the widespread belief that many American businesses are not assuming their full responsibility to fight inflation."

With labor already demonstrating what Kahn called "real... restraint" in its wage demands, yesterday's figures "put business on trial in the eyes of the American people," he said.

Meanwhile, Sen. Edward M. Kennedy (D-Mass.) complained in a speech to union leaders that the White House was not doing enough to control profits. "Who's keeping an eye on the oil companies' profits?" he asked.

Kahn has berated business in recent days, contending that the recent surge in industrial prices shows that small-and medium-sized businesses are not holding within the price guidelines.

At the same time, government figures show that wage increases won by key unions generally have been within the guidelines so far, although the Teamsters union appears headed for a breach.

William A. Cox, the Commerce Department's deputy chief economist, said that while some of the boost in profits stems from steep price hikes, the bulk merely reflects increased demand that pushed factories to near capacity.

Cox also cautioned against concluding that the fourth-quarter gross national product figure shows the economy still is overheating. He said the economy "has slowed down some" since those statistics were compiled.

The rise in before-tax profits last quarter amounted to 9.7 percent, pushing overall profits to a new annual rate of $225.3 billion, up from $205.4 billion. In the previous quarter, profits had remained flat.

After-tax profits also grew by 9.7 percent, to a new annual rate of $130.7 billion, from $119.2 billion before. In the third quarter, after-tax profits had declined by 1.1 percent.

Profits from current production, a more meaningful measure that is adjusted for replacement and inventory valuation, rose 7.1 percent, compared to a 1.1 percent rise in the previous quarter.

For 1978 as a whole, after-tax profits rose 25.2 percent.

The revision in the "real" gross national product figure -- to an annual rate of 6.9 percent in the fourth quarter of 1978, compared to 6.1 percent reported originally -- showed gains throughout the economy.

However, analysts noted an especially sharp pickup in business fixed investment, which rose at nearly a 9 percent annual rate, up from 6 percent in previous estimates.

Economists have been hoping for a rebound in business investment to help boost productivity and dampen inflation. Although recent surveys have shown business intentions still lackluster, some analysts expect a turnabout soon.

Yesterday's figures showed little real change in previous inflation estimates. The revised GNP price index, the government's broadest measure of inflation, was up at an 8.2 percent annual rate, compared to 8.1 percent before.

The fourth-quarter figures followed a lackluster performance in the July-September period, when the economy grew at only a 2.6 percent annual rate, following an 8.7 percent bounceback from the coal strike.