President Reagan yesterday decided that states can continue to tax profits earned overseas by multinational corporations that operate in the states. The practice has brought strong protests from U.S. and foreign corporations and European allies, who claim that it doubly taxes companies and inhibits foreign investment.

Reagan, after rejecting several proposals by a cabinet-level committee, decided not to file a motion to rehear a Supreme Court case decided in June, but to form a working group of government and business officials to explore the issue.

The taxation method was harshly criticized by British Prime Minister Margaret Thatcher, who is scheduled to meet with Reagan in Washington next week and is expected to bring up the dispute. The British government had hinted at possible retaliation if the result of the decision in the case decided against the Container Corp. of America was not changed.

A British Embassy spokesman said, "We're disappointed and further reactions must await" further study of the decision.

The issue put the president between his foreign and domestic political allies. The states claimed they had the right to the lucrative tax. In addition, a major party in the case was the state of California, where Reagan resides and where he served two terms as governor.

In a 5-3 ruling the court held that states can treat each corporation and its foreign subsidiaries as a combined worldwide company when computing the corporate tax base, instead of counting only what the company had earned within a state's borders. The states, according to a complicated formula, may then tax a proportion of the total, depending on the extent of the business conducted locally.

Foreign and American businesses have complained that the system allows them to be unfairly taxed twice on their profits. But officials of the Multistate Tax Commission have said the decision safeguards $600 million a year in revenue for the 13 states using the practice.

The federal government had voiced deep concern about the court's ruling. The United States does not tax the earnings of subsidiaries of foreign corporations, often because of reciprocal treaties that protect American firms overseas from the practice. The government had feared that the states' use of the tax method could threaten treaty obligations and lead to retaliation against U.S. companies.

Instead of asking for a rehearing of the case, Reagan announced he would establish a working group composed of members of the federal government, state governments and the international business community to explore the worldwide unitary taxation method and come up with recommendations. It was not clear yesterday whether members of foreign companies would be allowed to serve with the group.

Peter Welch, chairman of the Unitary Tax Campaign, a group of British-based international businesses operating in the United States, said he was disappointed with Reagan's decision and that the commission appeared to be a way for the president to duck the issue.

Welch said that on Thursday he asked Treasury Secretary Donald T. Regan, who is heading up the group, that the administration prevent taxation of foreign profits by the states and that no decision be made before Thatcher's visit next week. He said the group also asked that the administration file for a rehearing.

Netherlands Minister of Finance H.O. Ruding said in a telegram to Regan last week that the tax system poses "a very real danger" of foreign firms dropping plans to invest in the United States. The Japanese government earlier had asked the administration to "take appropriate measures as soon as possible to abolish the unitary tax system."

The working group is not expected to make a decision until sometime next year, Assistant Treasury Secretary John Chapoton told reporters. When asked if the decision would satisfy the British, he replied, "I think if they understand the seriousness with which we view their concern, there should be no retaliation."

An article yesterday stated incorrectly that President Reagan had decided states can tax profits earned overseas by multinational corporations. The president decided not to challenge a Supreme Court decision on June 27 that allowed states to use the unitary tax method, taking foreign profits into account in computing domestic profits for tax purposes. Also, the United States does tax subsidiaries of foreign corporations.