The Reagan administration plans to begin the controversial U.S. naval escort of reflagged Kuwaiti oil tankers through the Persian Gulf next Wednesday, congressional leaders said yesterday after a briefing by top administration and military officials.

In what amounts to a "very, very slow" start-up, the second escort operation has been scheduled for Aug. 6, with only two more planned before the end of August, House Armed Services Committee Chairman Les Aspin (D-Wis.) said after the meeting.

A senior White House official, saying that it was "very unfortunate" that Aspin had released what the official said was classified information, said that the date and details of the operation were likely to change because of the disclosure.

Both Aspin and Senate Minority Leader Robert J. Dole (R-Kan.) quoted Adm. William J. Crowe Jr., chairman of the Joint Chiefs of Staff, as saying the escort operation will begin next Wednesday, although Defense Secretary Caspar W. Weinberger was reported as saying earlier it might start as early as Monday.

Aspin said that the administration showed no signs of second thoughts about proceeding with the reflagging and escorts, administration proposals that have drawn congressional criticism. The gradual start was being made for operational not policy reasons, he added.

"The clear message was they were going ahead and they were not interested in messages from Congress for delay," said Aspin, referring to final appeals from some lawmakers, especially senators, for postponement of the operation.

The final go-ahead for the controversial plan to put 11 Kuwaiti tankers under protection of the American flag and U.S. warships came despite what Senate Majority Leader Robert C. Byrd (D-W.Va.) called "signals of concern and caution" from Congress, which nonetheless stopped short of action to block the operation.

While a majority of both houses have indicated they favor delaying the escorts, the Senate, facing a threatened Republican filibuster, failed for a second time yesterday to pass a resolution urging the administration to hold the operation "in abeyance" while other efforts to protect gulf shipping are pursued.

The measure was being considered in connection with trade legislation that Senate leaders are attempting to pass today. And opponents of reflagging said they will probably abandon efforts to invoke cloture if they fail again today on a stronger proposal designed to block the operation for 90 days. The House passed legislation calling for a 90-day delay earlier this month.

"I think we've come to the end of the road," said Sen. Jim Sasser (D-Tenn.). "We don't want to hold up the trade bill," said Sen. Dale Bumpers (D-Ark.).

Yesterday's vote was 53 to 40, seven short of the 60 needed to invoke cloture. The vote would still have been short of the mark if all Democrats had been in attendance, and it would take two or three more Republican votes to get cloture, said Bumpers, adding that such increased GOP support was unlikely.

The late afternoon meeting for Senate and House leaders of both parties was attended by Secretary of State George P. Shultz and Frank C. Carlucci, the president's national security adviser, as well as Weinberger and Crowe. It reflected commitments by Carlucci and White House chief of staff Howard H. Baker Jr. to keep Congress apprised of administration plans, although it was clear from the start that the administration did not intend to back off its reflagging plans.

At the White House earlier in the day, officials said the administration had new commitments of aid for the escorts from the United Arab Emirates and that the president was optimistic that both the Soviets and China would support a U.N. resolution calling for an end to the Iran-Iraq war.

The resolution is expected to come before the U.N. Security Council late this week or early next week. A senior administration official said there is "no linkage whatsoever" between the reflagging and the U.N. resolution. Some lawmakers had expressed hope that the U.N. effort might be seen as an alternative to the reflagging and escort operation.

An administration official said the new commitment from the United Arab Emirates was an agreement to allow overflights by U.S. aircraft, including AWACS radar planes, to give better warning of any potential attack on the tankers or escorts.

While Democratic leaders conceded inability to block the reflagging operation, Aspin and others said they had succeeded in slowing it, assuring better protection for U.S. escort forces and prompting solicitation of more cooperation from Persian Gulf countries.