PANAMA CITY, Panama (AP) _ American soldiers exchanged gunfire with intruders this week at the same fuel storage depot where similar shooting occurred in April, the U.S. Southern Command said.

No one was reported injured in the Tuesday afternoon and evening firefights at the Arraijan Tank Farm near Howard Air Force Base, the command said in a statement Wednesday.

It said there have been several intrusions since the beginning of June.

The statement said a Marine patrol encountered two armed intruders at 3 p.m. Tuesday outside the tank farm.

The intruders failed to heed an order to stop and fled into dense jungle when a Marine fired shots into the air, the Southern Command said.

Five hours later, a group of Marines patrolling the eastern side of the fuel depot ran into six intruders, two of whom were wearing night vision devices, the statement said.

The group began encircling the Marines, who ''determined the maneuver was hostile and opened fire. The intruders returned fire,'' the statement said.

The Marines and intruders exchanged another round of gunfire before the group stopped firing and fled, it said.

The command said the shooting incidents each ''lasted only several minutes in their totality'' in the span of about an hour.

The statement did not speculate on the intruders' identities. ''An initial search of the area only revealed footprints,'' and authorities were conducting ''a more detailed investigation,'' it said.

The 807-acre fuel storage depot is in a hilly, jungled area about five miles west of Panama City and about 1 1/2 miles west of Howard air base.

In April, the Southern Command contended there were four intrusions at the depot by what one spokesman called ''highly trained professionals.''

A Marine sentry was killed April 11 when fellow guards accidentally shot him as they were investigating the first of the alleged intrusions - by what the command described as eight men in dark uniforms.

Neither the Panamanian government nor its Defense Forces had any immediate comment on Tuesday's incidents.

In April, they ridiculed U.S. accounts of intrusions, saying the Marines apparently fired at ''swaying palm trees.''

The Defense Forces are commanded by Gen. Manuel Antonio Noriega, who was indicted in the United States in February on charges of trafficking in Colombian cocaine.

The Reagan administration has for months sought the ouster of Noriega, Panama's de facto leader, through a series of economic sanctions and unsuccessful negotiations.