Senate Majority Leader Robert C. Byrd (D-W.Va.), responding to President Reagan's criticism of Democratic initiatives on the Persian Gulf, accused the White House yesterday of "gross misunderstanding or a deliberate effort to confuse the situation."

Byrd's counterattack came as the Senate prepared for a showdown this week on a proposal by him and Armed Services Committee Chairman Sam Nunn (D-Ga.) to require congressional approval for long-term continuation of U.S. tanker-escort operations in the gulf.

In a statement last Friday vowing a veto of the legislation, Reagan said the Byrd-Nunn measure would "force a retreat from the Persian Gulf by the United States" that could ultimately lead to "our complete withdrawal from the Persian Gulf and the Gulf of Oman."

Byrd said Democrats support a continuation of longstanding U.S. military commitments in the Persian Gulf and are seeking only to apply constraints to reflagging and escorting of Kuwaiti tankers. That began last July in an attempt to protect the vessels from attack by Iran.

Rather than moving to invoke the 1973 War Powers Resolution, which could have limited all U.S. military operations in the gulf, Byrd said Democrats sought to target only the reflagging and escort operation.

Their measure would require the president to report within 30 days on the operation, including costs, goals and estimated duration. Within the next 60 days, or no more than 90 days after enactment, the operation would be halted unless Congress, by majority vote of both chambers, authorized continuation.

"Who knows? Congress might authorize {an extension} of this operation," Byrd said, adding that he might well support its continuation. The point, he said, is that the White House and Congress should share the decision.

"Why doesn't the White House want an equal partnership in this venture?" he asked. "Why does the White House want to go it alone?"

Democrats say they have the votes to pass the measure as an amendment to the defense authorization bill for next year or as a separate bill, although Republicans have not ruled out a filibuster or other delaying tactics to block passage.

The defense bill is under a veto threat because of provisions that limit testing and development of the president's Strategic Defense Initiative (SDI), also known as "Star Wars."

The Senate is expected to act on a long list of relatively uncontroversial amendments to the defense measure today before the showdown over the gulf and another contentious issue that could provoke a filibuster and veto confrontation: compliance with the unratified SALT II treaty.

Dale Bumpers (D-Ark.) plans to introduce an amendment to force the administration to abide by weapons limits in the treaty, which it breached last year. The vote on SALT II compliance is expected to be close, and the issue could trigger a filibuster.