Despite adverse weather and natural gas shortage in January and February the unemployment rate edged up only slightly last month, to 7.5 per cent from 7.3 per cent, the Labor Department reported yesterday.

The increase was less than most economists had expected.

The department also reported a big gain in the number of persons with jobs and said the average work week, which shrunk in January because of the cold weather and fuel shortages, rebounded last month.

But some efforts of the weather did show up in the February jobless report. Most of the increased unemployment figure - 225,000 persons - was due to factory layoff caused by fuel shortages, and the number of persons working part-time because of the weather grew sharply.

On balance, however, yesterday's report tends to support Carter administration economists who have urgued that the cold and gas shortages would have a big but temporary impact on the economy.

It appear that most of the impact of the cold weather and gas shortages came after the January unemployment survey and dissipated before the February survey.

The Labor Department conducts its unemployment survey each month during the week containing the 12th day.

Some economists and members of Congress had argued that the winter's disruption of the economy was so great that the higher fuel bills, layoff and production declines would negate the impact of President Carter's proposed economic stimulus program.

Testifying before the House Budget Committee yesterday, Charles L. Schultze, chairman of the Council of Economic Advisers, said that while the growth rate in the first three months of the year would be lower than expected, the economy will rebound and grow faster than originally predicted in the second three-month period.

Schultze said that "we see no need for an extra fiscal push from the government" to overcome the cold weather effects as some had argued last month.

Nevertheless, while the economy has improved at a good pace in recent months and 3.9 million more persons are at work now than at the worst part of the recession in April, 1975, the 7.5 per cent unemployment rate is high.

During the four previous postwar recessions, the unemployment rate never got as high as 7 per cent.

In January, the unemployment rate fell sharply to 7.3 per cent from 7.8 per cent in December, but most of the decline came about because 450,000 persons dropped out of the labor force.

Since the unemployment rate is the percentage of the labor force - those with jobs and those actively seeking them - without jobs, a decline in the size of the labor force can trigger a decline in the unemployment rate.

Commissioner of Labor Statistics Julius Shiskin told the Joint Economic Committee that the "labor force bounced back in February."

"The February increase in the labor force was made up of an increase of 404,000 in employment and 225,000 in unemployment," Shiskin testified. He said that a special survey indicated that employment would have been higher by nearly 100,000 "if it weren't for energy problems that existed."

Shiskin said that the rise in unemployment can be explained in part by energy problems because nearly all of the increase in unemployment came about among persons who were laid off.

The Labor Department reported that the number of persons involuntariy working part-time rose by 220,000 to 1.3 million. "Nearly all of this increase was attributed to material shortages steaming from energy and weather-related problems," the department said.

The unemployment rate is based ona monthly survey of 47,000 households. It showed total employment of 88,962,000 and total unemployment of 7,183,000 in February. Unemployment rates for nearly all groups - men, women, blacks, heads of households and full-time workers - rose slightly. Teenage joblessness fell from 18.7 per cent to 18.5 per cent.

Another survey - of employer payrolls - is considered more reliable but less inclusive than the 47,000 households survey. The payroll survey showed a net gain in nonfarm employment of 259,000 persons to a total 80,818,000.

The employment rate is adjusted to take account of regular seasonal ups and downs. Some economists think the severe recession distorted the seasonal adjustments into understanding joblessness early in the year and overstating it later in the year.