WASHINGTON (AP) _ The Supreme Court today let stand a ruling that police officers need court warrants before they call criminal suspects out of their homes to arrest them.

The court, turning down a Justice Department appeal, refused to rule on what government lawyers called ''the single most important unresolved issue in arrest law.''

The government's appeal also raised the possibility that the justices could use the Tennessee case to carve out a major exception to the so-called ''exclusionary rule'' on criminal evidence.

The exception would allow in criminal prosecutions the use of evidence seized unlawfully by police officers who ''reasonably'' but wrongly believed they were not violating anyone's rights.

The appeal acted on today stemmed from the June 13, 1982 arrest of John Henry Morgan at his mother's home in Harriman, Tenn.

Morgan County Sheriff Roger Reynolds and a deputy, Teddy Bells, earlier that day had gone to Potter's Field, a public park, to investigate complaints about men shooting guns.

Entering the park, they heard the fire of automatic weapons. The law officers saw Morgan and four or five other men gathered around a car's open trunk.

The two officers left the park and called for help after being told by a bystander that the group had threatened to ''kill any law that ties to arrest them.''

The bystander also told Reynolds that the car was filled with machine guns, pistols and shotguns.

When the Reynolds and Bells returned to the park with other officers Morgan and the other men had left. The sheriff's department then broadcast an alert for the car.

A Harriman police officer saw the car and followed it to the home of Morgan's mother. He said he saw several people carry weapons into the house.

Darkness had fallen by the time nine police officers in several patrol cars surrounded the house. They called for Morgan to come out.

Morgan was formally arrested and charged with the federal crime of illegally possessing a gun after he came out of the house.

A federal trial judge suppressed all evidence gathered by police at the house, including the gun Morgan is charged with possessing illegally. The judge said the officers should have obtained an arrest or search warrant before going to the home because no emergency existed.

The 6th U.S. Circuit Court of Appeals upheld the judge's ruling last Sept. 13, finding that Morgan ''was illegally arrested when the police surrounded the ... home and ... induced his presence at the door.''

A 1980 Supreme Court decision bars police, unless some emergency exists, from entering anyone's home to make an arrest without a court warrant.

But police traditionally have been free to make warrantless arrests outside a home if ''probable cause'' exists to believe the suspect committed a crime. The 6th Circuit court said the government was wrong in contending that no warrant was needed to call Morgan out of the house.

''The important consideration ... is the location of the arrested person, and not the arresting agent, that determines whether an arrest occurs within a home,'' the appeals court said.

In seeking Supreme Court review, Justice Department lawyers argued that requiring police to obtain warrants ''in all of these very common situations will impose substantial and unnecessary costs.''