The dollar rebounded sharply on overseas money markets yesterday as key foreign governments threw their support behind President Carter's dramatic steps to halt the slide of the U.S. currency.

West Germany Chancellor Helmut Schmidt voiced his immediate support for the U.S. actions, claiming his government played a role in shaping the new U.S. economic policy.

Karl-Otto Poehl, vice president of the West German Bundesbank, called the U.S. actions "very strong." He predicted, "America now has enough weapons to fight" the dollar slide.

In France, where the dollar had dropped more than 20 percent in value against the franc in recent weeks. Prime Minister Raymond Barre called the Carter action "courageous."

An in Japan, Carter's program was seen as a stabilizing measure. In a brief statement, Japanese Finance Minister Tatsuo Murayama said, "We are sure that joint intervention by the Japanese and U.S. and other government in the foreign exchange market will help stabilize the international monetary situation."

More important to the Carter administration, the new program had an immediate impact on foreign money markets.Although yesterday was a bank holiday in many European nations, the dollar showed sharp gains on almost every market that was open.

In Frankfurt, the dollar gained nearly 5 1/2 percent against the mark. It closed at 1.8450 marks compared with Tuesday's 1.73. In Zurich, the dollar closed at 1.5725 Swiss francs against Tuesday's close of 1.4840 francs.

Because trading was completed on the Tokyo market by the time of the announcement, there was no immediate reaction. The dollar had dropped in trading there to 176 yen Tuesday but had risen to close yesterday at 178.80 yen.

When the market opened early today, however, the dollar soared more than 9 yen to 188 yen, then edged off slightly and was trading between 185 and 186 yen a few minutes after the opening.

In New York yesterday, the value of the dollar had soared to 185 - reaching 191 yen at one point during afternoon trading. Other New York trading results showed the dollar up to 1.8850 West German marks and 1.58 Swiss francs.

Prime Minister Barre, considered one of the France's best economists, said the new Carter program has "every chance of contribution to the righting of the currency of the United States." He said he hoped the immediate reversal of the dollar on international money markets would lead "to the stability and the monetary security that are indispensable to the amelioration of economic activity and employment in the world."

French officials said that Treasury Secretary W. Michael Blumenthal had informed Economy Minister Rene Monory in advance of the U.S. actions. Monory's reaction was described as "positive."

There was no immediate, official reaction from Great Britain to the Carter Program, but foreign exchange dealers in London generally welcomed the U.S. action. Carter, one dealer predicted, has "restored some sanity to exchange rates. But why did he wait so long?"

Like other European trading centers, the dollar staged an almost chaotic comeback against all currencies.

The widespread view in London was that the dollar had been badly oversold and markets had behaved irrationally in driving it so low. Money men believed that a short, sharp increase in interest rates would set things right. They read the Carter measures yesterday to mean that this will take place.

Some skeptics had figured that Carter would wait until after the mid-term Congressional elections before taking any action. But as some observers noted yesterday, the political judgment of money men often matches the financial judgment of political experts.

For Carter, however, the most critical reaction yesterday was the approval of West Germany - the dominant European economic force.