CAPE CANAVERAL, Fla. (AP) _ Even the captain of an eavesdropping Soviet spy ship seemed impressed by the first successful launch of the Navy's deadly new Trident 2 missile from a submerged submarine.

''My best regards to the skipper of the sub,'' the Soviet captain radioed after the 44-foot missile roared away from the USS Tennessee, burst to the surface, ignited and hurled a dummy warhead to a target far down the Atlantic tracking range on Wednesday.

The message was radioed to the launch support ship Range Sentinel. Earlier, the Range Sentinel had warned the Russian trawler not to get too close.

''We're not going to interfere with the launch,'' replied the captain of the Soviet ship, and he stayed about 2 1/2 miles away, just outside the security zone.

For years, Soviet spy ships have observed most launchings from Cape Canaveral.

Greenpeace U.S.A. activists who oppose nuclear weapons at sea halted the launch attempt last Friday by sailing ships into the security zone and refusing to leave, arguing they were in international waters. They stayed away Wednesday, saying they had made their point.

Following the 11 a.m. launch, Rear Adm. Arlington Campbell, commander of Submarine Group 6, told reporters on the Range Sentinel: ''As far as we can tell from our telemetry, it was a totally nominal launch. From all indications, everything has been successful.''

The Navy did not disclose how far the warhead section traveled.

Each of the $23.7 million missiles is designed to propel as many as 12 nuclear warheads to different targets more than 4,600 miles away.

The results were far different from those of the Trident 2's first submarine launch on March 21, when the missile cartwheeled out of control and exploded just four seconds after it was launched from the Tennessee.

Investigators reported that failure was caused by a faulty mechanical linkage responsible for moving the rocket motor nozzles back and forth to control direction. The system was redesigned.

''We had one failure at sea,'' Campbell said. ''But these are production evaluation missiles. We're here to learn. They get improved so they are right when they are actually deployed.''

The Navy plans seven or eight more underwater tests over the next few months. If all goes as planned, the Navy will send the Tennessee on operational patrol next March with 24 of the nuclear-tipped missiles.

Before the Trident 2 was taken to sea, the Navy conducted 19 flight tests from a land launch, rating 15 of them successful.