WASHINGTON (AP) _ Mother Teresa, the elderly Roman Catholic nun from Calcutta, India, who serves the sick, dying and destitute, received the Medal of Freedom on Thursday from President Reagan, who called her a ''citizen of the world.''

Mother Teresa told Reagan, his wife Nancy and about 150 guests in the White House Rose Garden that she personally was unworthy but was accepting the honor in the name of the millions of poor people in the world to whom she has dedicated her life.

The short, wrinkled nun used similar words in accepting the 1979 Nobel Peace Prize and numerous other honors for her charitable work.

Reagan noted that Mother Teresa was a month late in receiving the Medal of Freedom, the highest U.S. civilian decoration. Her medal was to have been presented with a dozen others on Mayh 23, he said, but ''Mother Teresa was busy as usual saving the world - and I mean that quite literally.''

Referring to the 74-year-old nun standing at his side, Reagan said, ''The goodness in some hearts transcends all words and all nationalistic considerations. Some people - some very few - are in the truest sense citizens of the world.''

Quoting from the citation for her award, Reagan said, ''Most of us talk of kindness and compassion, but Mother Teresa, the 'Saint of the Gutters,' lives it.''

Referring to the nun's dedication to the poor, the president said jokingly it would not be surprising if she melted down the medal of gold and silver alloy to ''try to turn it into something to help the poor.''

He praised her for providing ''a radiant example'' that has inspired ''so many Americans to become personally involved in helping the poor.''

Thanking Reagan for responding last year to her personal appeal for U.S. food aid for starving Ethiopians, Mother Teresa said that until then, ''I never realized you love the people so tenderly.''

''I can tell you that the gift that has come from your people has brought new life to our suffering people in Ethiopia,'' she said.

Mother Teresa also thanked American Catholics ''for their continued and delicate love they have shown by giving their children to become sisters and their help to save the poor throughout the world.''

The Missionaries of Charity she founded decades ago in India to help the ''poorest of the poor'' now operates worldwide. With foreign help, she said, ''we are no longer alone. ...Together we are doing something beautiful for God.''

Mother Teresa canceled speaking engagements in Boston and Washington this week, complaining that she needed rest, but told a reporter Thursday she was feeling much better.

She said she intends to visit Jordan, Egypt and Sudan on her way back to India.

From the White House, Mother Teresa went to George Washington University Hospital a few blocks away to visit a patient suffering from acquired immune deficiency syndrome. The AIDS patient, whom the hospital did not identify, had written the nun requesting a visit while she was in Washington.

Mother Teresa visited four AIDS patients in hospital, distributed medals and prayer cards to patients and staff members and toured the hospital's maternity ward, said hospital spokeswoman Irene Haske.