The Reagan administration must reduce sharply its huge budget deficits, which cause high interest rates, or be saddled with the blame for not only an aborted global recovery, but also a continuing Third World debt problem, the Bank for International Settlements at Basle said yesterday.

In its annual report, the BIS--sometimes called "the central banks' central bank"--asserted that high U.S. interest rates are "damaging," and that the responsibility for getting them down "clearly falls on the U.S. authorities, and squarely on the shoulders of those in charge of fiscal policy."

The report also warned that there could be a second wave of trouble on the international debt front, characterizing the rescue packages put together last year and early this year as "holding operations" that provided "a vital breathing space" and that now must be followed by concerted action.

It stressed that the debt situation "cannot be kept within manageable bounds without the effective participation of private banks," urging that the banks maintain "steady nerves" and "not withdraw from new international lending."

Lower interest rates would be a tonic for the hard-pressed Third World debtors, the report pointed out. It warned that, while an international debt crisis may have been averted so far, "The world's financial system remains basically fragile."

The annual report went on to say that, "From every conceivable angle, the most important and most urgent task for policy is to exert downward pressure on United States interest rates."

Nonetheless, taking a broad look at the world's economy, the BIS found some cheer in the gains that were registered last year in the fight against inflation. It more or less echoed the theme put forward recently by the Organization for Economic Cooperation and Development, that policy makers now should have more room to focus on growth.

The report stated publicly the concern voiced diplomatically by all European governments at the Williamsburg economic summit on the dangers of the huge U.S. budget deficits.

The report called on the Reagan administration to take measures assuring the reduction of the "structural" budget deficit, "preferably in the field of expenditure, but also, if necessary, in that of taxation." The Williamsburg declaration merely called for budget reduction--but at American insistence, referred only to expenditure reduction, and not to raising taxes, which is a touchy domestic American political issue.

The BIS report argues that an American initiative to reduce interest rates "could increase the scope for policy maneuver" in Japan, West Germany and Great Britain, where signs of economic revival also have appeared. If, then, there were a recovery in four major countries, there would be automatic relief to "the debt-ridden economies of the rest of the world," it says.