Rosalynn Carter began a seven-nation tour here today as the personal envoy of the President, who, in his sendoff this morning, stressed his "special commitment to strengthening our relationships" with Latin America.

Mrs. Carter arrived here under overcast skies and told Jamaican Prime Minister Michael Manley, who greeted her at the airport, "We want to consult closely with you and strengthen our ties of friendship, as you strive for more social and economic justice."

Her visit here was the first stop of a 12,000-mile, 14-day goodwill tour that also includes Costa Rica, Ecuador, Peru, Brazil, Colombia and Venezuela.

Hundreds of schoolchildren lining the road outside the airport shouted greetings and waved green-yellow-and-black Jamaican flags. At one point Mrs. Carter stopped her motorcade, and she and Manley got out and talked with the youngsters.

Earlier, she had accompanied to the Brunswick, Ga., airport by her husband and their daughter, Amy. The airport is near St. Simon's Island, where the family spent the weekend.

The President said that in addition to expressing friendship, Mrs. Carter would be discussing "subjects of interest" to the foreign leaders and would be cabling daily reports to him and Secretary of State Cyrus Vance.

"We don't have a special slogan for Latin America any more," said the President, referring to the "Good Neighbor Policy" of Franklin D. Roosevelt and "Alliance for Progress" of John F. Kennedy.

"But we have a commitment to treat (the countries) as individuals," Carter added. "One of the problems of the past has been that we've looked on South America, Central America, th Caribbean, as part of a homogeneous groups of nations." He said that each country has "special individual problems and special opportunities in relation to us."

Mrs Carter, he said, "will deliver to each leader my good wishes and my special commitment to strengthening our relationships with them in a friendly and equal fashion. They are just as valuable to us as we are to them."

After her husband spoke, Mrs. Carter said she thought she could "establish a personal relationship" with leaders she is to meet in the next two weeks.

She said she wants her journey "to be more than a goodwill trip. I want it to be valuable to the countries. Therefore I have studied. I do know Jimmy's basic foreign policy, which I will be stressing to the foreign heads of states, and I will be consulting with them and bringing back their concerns and special problems."

After arriving here, Mrs. Carter attended a "workinglunch" with Prime Minister Manley, paid a courtesy call on Governor-General and Mrs. Florizel A. Glasspole, attended a U.S. embassy reception, and went to a buffet supper given by the prime minister.

A U.S. official traveling with Mrs. Carter said she had told Manley that the United States is discussing ways to help with Jamaica's severe economic problems if the country takes belt-tightening steps to reduce its budget deficit.

Jamaica, which is slightly smaller than Connecticut, has a 25 per cent unemployment rate and a virtually bankrupt economy. Upper and middle-income Jamaicans have been leaving in record numbers since Manley raised taxes sharply and began to nationalize farms and factories.