The Environmental Protection Agency moved yesterday to relax slightly restrictions on the levels of smog permissible in the air over the nation's cities, despite objections from some of its own experts.

At the same time, the agency said it would issue a modified set of clean air requirements that some administration economists had critized for excessive costs. EPA officials said they had agreed on a change suggested by President Carter's economic advisers in an effort to hold down those costs.

EPA Administrator Douglas M. Costle said the maximum acceptable smog levels would be raised from .08 parts per million to .10 parts per million in the air. Costle said the increase would leave a margin for safety between dangerouly polluted and acceptable air quality.

Noting that there had been"considerable debate" over the increase in smog level, EPA air quality chief David Hawkins said that while he personally opposed the move, the action was still "a responsible proposal."

The proposed alteration in the air quality standard for smog was also opposed by a special advisory panel set up by EPA to study acceptable smog levels andby several environmental groups.

Hawkins said, however, that despite the objections there was evidence that harmful effects from smog on humans such as chest tightness and coughing do not occur until smog reaches the level of .15 parts per million in the air.

He said the change could save as much as $1 billion anually in auto emission and stationary source pollution cleanup costs to cities and would allow dozens of U.S. cities that wouldn't have met the restrictions under the existing standards to meet smog pollution standards by 1987.

"There will be no cause for less stringent auto emmission standards or reduced emphasis on control of other emission sources such as gasoline stations, oil refineries and other sources of hydrocarbons or ozone," said Costle.

EPA also said it was issuing an additional set of clean air requirements for new sources of pollution that some Carter administration economic experts have predicted could cost as much as $300 million annually in compliance charges for business.

Hawkins said the rules governing deteriorating of air quality in pristine areas would cover about 1,600 businesses annually. He said an administration suggestion to remove another 2,400 new businesses from the requirements was accepted by EPA on the grounds that this would increase polution by only about 2 percent, but would cut the cost of the program significantly for the business sector.