Two small Soviet warships deliberately bumped two U.S. Navy ships steaming through the Black Sea within nine miles of the Crimean coast yesterday in a test of what constitutes Soviet territorial waters, according to the Defense Department.

No serious injury or damage was inflicted by the slight collisions, Navy officals said. They said this was the first time in memory that the Soviets bumped ships in the Black Sea, although the Soviets protested a 1986 U.S. patrol in the same area. Washington and Moscow each blamed the other for provoking yesterday's collisions, and the United States called Soviet Ambassador Yuri Dubinin to the State Department yesterday morning to protest.

The Navy mission called for the destroyer USS Caron and the cruiser USS Yorktown to exercise the "right of innocent passage" by sailing past the Crimean peninsula inside the 12-mile limit that Moscow claims as territorial waters, according to the Pentagon. The United States claims a three-mile territorial limit.

Shortly before 11 a.m. (3 a.m. EST), the Navy said, one of the Soviet skippers steaming east off Crimea radioed this warning to the U.S. ships: "Soviet ships have orders to prevent violation of territorial waters. I am authorized to strike your ship with one of ours."

"We made no response on {the radio}," Capt. Gerrish C. Flynn said at a Pentagon briefing. "Our response was to continue on course and speed, which is what any prudent mariner would do." Flynn said a Soviet Badger bomber flew over the ships, apparently keeping track of the movements of both navies.

The Caron, a 7,800-ton Spruance-class destroyer, kept steaming east nine miles off Crimea near the Soviet port and naval base at Sevastopol. A 1,100-ton Soviet Mirka-class frigate, also going east, swung into the Caron and bumped along the bigger ship's left side, according to the Navy. At about the same time, the Navy said, a 3,900-ton Soviet Krivak-class destroyer executed the same scraping maneuver against the left side of the 9,600-ton Yorktown, steaming east 11 miles from the Crimean coast.

"Both ships encountered very, very slight damage," Flynn, a Navy planning director, said. "Essentially they were just grazed on the side. . . . Both ships are operating routinely in the Black Sea as planned."

At the State Department, spokeswoman Phyllis E. Oakley said "there is no justification for the Soviet action which endangered lives and ships, and we have protested the actions in the strongest terms. Undersecretary of State Michael H. Armacost called in Ambassador Dubinin this morning to lodge our strong protest. There is no question of our legal right to operate our ships in the manner and at the location where the USS Yorktown and Caron were operating at the time of the incident. . . . We intend to continue exercising our rights under international law."

Dubinin told reporters later that the two American ships "violated the state border in the area of the southern coast of the Crimean peninsula. The ships did not react to the appropriate signals by our border patrol. They were engaged in a hazardous maneuver, which resulted in a collision with Soviet ships. The actions of the U.S. ships are viewed as deliberate provocation. For these reasons, we have strongly declined the U.S. protests."

The Caron and Yorktown "were exercising the right of innocent passage through the Soviets' 12-mile territorial sea," Navy Cmdr. Richard Schiff, a legal adviser, said. "They engaged in no activity prejudicial to the security of the Soviet Union. The presence of the ships in the Soviet territorial sea was part of our assertion-of-rights program."

White House spokesman Marlin Fitzwater said that President Reagan had been notified of the collisions early yesterday morning and "has received a full briefing on the incident."

There was a similar Black Sea confrontation on March 19, 1986, between the Caron and Yorktown and the Soviets, but no collisions occurred. The Caron and Yorktown came within six miles of the Soviet coast, according to the Pentagon. Soviet leader Mikhail Gorbachev filed a protest with the U.S. Embassy in Moscow at the time.