The Environmental Protection Agency pleaded with the nation's schools yesterday to start new asbestos inspections immediately, warning that procrastination until next summer will mean they will not meet the deadline for a new federal law.

There will not be enough trained inspectors or asbestos program writers if too many districts let the work slide until the long vacation, Susan Vogt, deputy director of the agency's Office of Toxic Substances, said at a news conference to unveil EPA's final school asbestos rules.

The new rules require the roughly 45,000 public and private school districts in the nation to inspect their 107,000 buildings for asbestos and decide what, if anything, to do about it.

As of April, EPA-approved courses had trained 5,000 inspectors.

In a major addition to current requirements, inspections must cover both the dangerous crumbly kind of asbestos that can throw off breathable fibers and other kinds that would be safe if undisturbed, such as floor tile.

Asbestos, if breathed, can cause lung cancer and other disorders that may not develop for 40 years. The risk to children is a concern because asbestos was widely used for insulation in the past and because fibers lodged in children's lungs have a longer time to do damage.

A 1982 EPA rule required inspection only for breathable asbestos and notice to parents and employes if any were found.

About 30 percent of the nation's school districts had not fully complied with the rule, EPA estimated, and the agency conceded that many had used incompetent removal contractors.

Under the new rules, inspections must be made by people who have passed an EPA-approved course. All districts must submit an asbestos management plan, written by someone who has passed another EPA-approved course, to state governors by Oct. 15, 1988.

The EPA may impose a $5,000-a-day penalty for violations.