The new Diplomatic Relations Act was signed into law Saturday by President Carter. When it goes into effect at the end of December it is expected to reduce substantially the level of diplomatic immunity from civil and criminal prosecution that foreign diplomats and their staffs have enjoyed since 1790.

The old statute gave blanket protection to all embassy personnel, technically making it a crime even to bring suit against them.

"We procrastinated far too long," said Sen. Charles McC. Mathias (R-Md), who introduced the bill in the Senate. "The old statute failed to distinguish between ambassadors and bottlewashers in embassies . . .

"American citizens," said Mathias, "have in some instances been tragically maimed for life and been unable, as a matter of right, to obtain damages or even their medical expenses."

The new law requires diplomats to carry liability insurance under guidelines to be established by the president. It also prohibits insurance companies from using their clients' immunity to avoid payment of claims.

"I'm just delighted that this is now the law of the land," said Rep. Joseph L. Fisher (D-Va.), who sponsored the bill in the House. He said he was glad that the United States finally has regulations for diplomats in line with most of the rest of the world.

In addition to its insurance provisions, the new law adopts the Vienna Convention of 1961, which makes diplomats, their staffs and families more or less legally accountable for their actions dpendening on their ranks.

Roughly 12,000 diplomats and their close relatives in Washington and New York will continue to enjoy full criminal immunity and civil immunity except in cases of business dealings outside their official roles.

Lower ranking embassy staffers, however, will continue to enjoy all immunities only while on embassy business. Otherwise the roughly 10,000 members will be subject to civil suits.

The families of about 3000 service personnel - janitors, chauffeurs and the like - are subject to all legal proceedings.