Leading with an expression of regret from President Reagan, the United States today attempted to calm growing Japanese anger about the sinking of a Japanese freighter by a U.S. nuclear submarine but it told Japan to be patient and not expect immediate results from an investigation.

Reagan sent his personal regrets to Prime Minister Zenko Suzuki and said he expects "sufficient progress" would be made in resolving the incident before Suzuki's visit to Washington next month.

But his message was accompanied by a personal appeal from Ambassador Mike Mansfield for patience in investigating the freighter's sinking and a promise that the facts would not be covered up. Immediately following announcement of the collision last week, Mansfield had sent a message conveying Reagan's regrets to the foreign minister.

Despite the accommodating tone of the U.S. messages, it is questionable whether they will stem the outpouring of anti-American public sentiment aroused by the freighter's sinking and the loss of two lives.

Neither message met the Japanese government's request for a prompt explanation of the sinking and the alleged abandonment of the crew. Mansfield told Foreign Minister Masayoshi Ito bluntly that a piecemeal disclosure of evidence could prejudice the investigation and any litigation that might grow out of it.

The U.S. Navy is investigating the accident, which occurred 10 days ago. But if all normal procedures are followed, a report may take several months, military sources said.

The Japanese government is under unusually strong public pressure to obtain a quick explanation and has asked for an interim report, something American officials say is probably impossible to produce in a way that would answer all the questions.

The sinking blew up into a full political controversy early this week, with both opposition and government party politicians demanding an early resolution. Major newspapers have published tough editorials accusing the American sub of abandoning the Japanese survivors and implying strongly that the U.S. Navy intends to cover up the facts to protect military secrets.

There are also charges that the pro-American government is treading too softly in demanding an American explanation.

There have been suggestions that the prime minister might be forced to call of his visit to Washington next month, but he has said instead that he will raise the issue with Reagan.

The captain and the first mate of the freighter Nissho Maru were drowned when the ship was rammed and sunk by the USS George Washington in the East China ysea. For 19 hours the surviving 13 crewmen drifted in lifeboats and later told reporters they had seen the U.S. submarine surface after the collision and an American patrol plane circling overhead.

Japan has demanded answers to three questions: how the collision happened, were survivors ignored, and why the U.S. Navy did not acknowledge the accident for nearly 36 hours.

The Navy said the sub's crew never saw a ship or survivors in distress but it has not explained the long delay in disclosing the collision.

Mansfield this morning promised Ito a complete investigation but stressed the legal rights of the officers and crew members of the submarine.

A Japanese version of Mansfield's comments was given reporters by Shinichiro Asao, director general of the Foreign Ministry's North American bureau.

At one point, he said, Mansfield reminded Ito that "the United States is a country ruled by law" in which the rights of individuals are protected and the sub's captain and other crew members might have their lives and careers affected by a premature disclosure.

Mansfield said that if one part of the evidence is revealed before a complete report is made public it might make it impossible to gather further evidence and courts might find it difficult to render a judgment. He promised that the issue of compensation for the freighter and its crew would be handled separately from the Navy investigation and that claims from survivors and the ship's owners would be accepted promptly.

Mansfield also said, according to Asao, that as a former U.S. Senate majority leader he could understand the "severe" political pressure Ito is under. But he said that should not lead to interpretations of the accident on the basis of incomplete evidence.

Under questioning by reporters latter, Ito said he did not regard Mansfield's comments as a categorical refusal to provide his government with an interim report on the collision.

Reagan's letter expressed particular regret for the loss of two lives.

"You may be assured that the resolution of this incident is receiving my personal attention, and I have every expectation that sufficient progress will be made prior to your Washington visit to satisfy the requirements on both sides," it said.