The power of a single multinational company to enlist the support of the American government for its own special cause and even affect relations between the United States and another country was vividly illustrated during President Carter's visit to Nigeria a week ago.

The fate of an arrested American insurance executive and his company's problems with the Nigerian government narrowly missed becoming an item on the official agenda of issues Carter took up with Nigeria's chief of state, Lt. Gen. Olusegun Obasanjo, according to American sources involved with the case.

The parent company, American International Group of New York, used all the influence it could muster with the State Department and White House to get the president to take up its local problems with Obasanjo, according to these sources.

The bid was foiled, however, by the U.S. Embassy here and by presidential aides who did not want the special cause of a single American company to mar the larger objectives of Carter's trip here, namely marking without mishap the first state visit by any U.S. president to black Africa and consolidating the new American-Nigerian friendship.

"This matter had no effect on the conduct or results of the president's visit," the U.S. ambassador to Nigeria, Donald Easum, told American reporters afterward.

Nevertheless, just how the American insurance company was able to gain so much special attention for its problems here is not altogether clear. Sources, however, describe the firm as exceedingly "aggressive" in its business practices both in Nigeria and elsewhere and management was obviously ready to exploit the Carter visit to its own best advantage.

[It also remained unclear why high-level officials of the Carter administration allowed themselves to become embroiled in the controversy during a presidential visit to an important African nation, Washington observers noted. At the least, it appeared to these observers to be another sign of the administration's sometimes unorthodox approach to foreign policy that some critics have labeled as amsteurish].

Using its influence at the top of the U.S. political establishment the American International Group got Nigeria to release Louis Lefevre, the manager of its local subsidiary, from prison at the end of the Carter visit. Lefervre, 21 in connection with alleged business malpractices.

Further, secretary of State Cyrus Vance devoted half an hour of his talks with his Nigerian counterpart, Brig. Gen. Joseph Garba, to a discussion of the Lefevre case and the American press took up the issue puring President Carter's three day visit.

"It became very obvious to the president's party that if Mr. Lefevre was still in jail when he got home, President Carter would have to answer some questions because this thing was not going to disappear, said a vice president of the parent New York company who asked not to be identified during an interview at the lefevre home on Ikoyi Island in Lagos, last week.

In addition, the Lefevre affair attracted considerable public attention to the larger issue of the overall climate for American investment in Nigeria today. U.S. officials said that they were hopeful the result of the president's visit would be a improvement in nigeria's handling of American companies.

Specifically, they would like to see Nigerian ease its policy of seeking 60 percent interest, and sometimes 100 percent, in major American companies operating here. This policy has already provoked Citibank into leaving the country and IBM is reportedly on the verge of following suit.

Other sore points for American companies have been lack of consular access to several detained American businessmen and restrictions on the amount of money a firm can remit abroad each year - 16 percent of its total capital value.

Ambassador Easum insists that the Lefevre affair was an exception and that it should not prejudice American companies against investing here. "American businessmen should not be distracted by isolated incidents of this nature in their evaluation of the Nigerian investment climate," he said.

He nonetheless urged them to make a "thorough evaluation" of the Nigerian market before going ahead with any investment or sale of goods. American businesses, primarily the oil companies, already have a $1.2 billion stake in the rapidly expanding Nigerian economy and another 30 companies are reportedly planning to come here.

Obasanjo is said to have assured President Carter that he wants more U.S. investment and to have described the present climate as "propitous" for it.

Lefevre was first detained for about a week on March 21 and questioned about a loan of more than $700,000 by his company, the American International Insurance Company of Nigeria, to a construction firm. The Algerians claimed the loan was not properly secured.

Lefevre was eventually charged with stealing and conspiring to steal money from his own company and violating Nigerian foreign exchange regulations.

After posting $7,500 bond, he was released from lkoyi prison the day before Carter arrived only to be rearrested under a special 1967 decree the next day. He was released again on April 3, a few hours after Carter left.

He is now awaiting a hearing. A parent company executive dismissed the charges and "far-fetched" and "cooked up" and said he felt it was "fairly remote" that the Nigerian government would press the charges.

The Nigerians have made no official comment on the case.

The roots of the Lefevre affair go back to his ongoing quarrel with the Nigerian government over the amount of money offered in 1976 for a 49 percent interest in the company, which is the second largest life insurance company operating in Nigeria.

Lefevre said the government offered him only par value for 25,000 shares, or about $83,000, which he estimated was about 5 percent of annual earnings. The Nigerians offered him about $3.30 a share, while an independent London firm put the value at $83, according to the company manager.

After more than a year of haggling, American International accepted the government terms under protest. None of the other 12 foreign insurance companies affected by the Nigerian measure protested the governments compensation terms, however.

Then last November the government announced that it wanted a total of 60 percent interest in foreign insurance companies, or another 11 percent, reopening the whole question of debate on terms.

To make matters worse, Lefvre first refused to promote, and then fired, one Nigerian in the company who he subsequently discovered belonged to "an old and influential family" from Ibadan with friends in high government circles.

A government-appointed arbitrator looked into the case and ruled against Lefevre, asking him to reinstate the Nigerian. He refused and, as Lefevre himself puts it, "two issued fused and flames flared up."

Whether the flames are dying out now is not altogether clear. In any case, Lefevre says he is scheduled to leave Nigeria for a post in the Philippines as soon as his court case is disposed of.