Patil, who completed her two-day visit to Luang Prabang today, left Vientiane yesterday after holding talks with top leaders of the country.
She was accorded a traditional welcome by dancers and drummers at the airport.
The president visited the National Museum, which was earlier the palace of Lao King Sisavang Vong and his family in 1904.
The palace was converted into a museum when the monarchy was overthrown in 1975 when Savang Vatthana and his family lived there.
Governor of Luang Prabang Bouheuang Douangphachanh called on the President and hosted a banquet in her honour in the evening.
Baci ceremony, a traditional ritual by Laotians to accord a welcome and pray for a person's well-being, was performed in Patil's honour here.
"It is a ceremony to celebrate a special event, whether a marriage, a homecoming, a welcome, a birth, or one of the annual festivals.
"A mother is given a Baci after she has recovered from a birth, the sick are given Bacis to facilitate a cure, officials are honoured by Bacis, and novice monks are wished lunch with a Baci before entering the temple," a local said.
The ceremony involves tying of a white sacred thread on the hands of the people involved in it.
On Sunday, Patil visited the Xiengthong temple in Luang Prabang and offered prayers with her husband Devisingh Shekhawat.
Known as the temple of the Golden City, it was built around 1560 by King Setthathirat, who ruled Laos from 1548 to 1571.
Till 1975, when the country was ruled by monarchs, Xiengthong was a royal temple where kings of Laos were crowned.
Later, Patil enjoyed a one-hour boat ride on the Mekong river, which forms the life-line of this part of the world.
The President was given a warm send-off and she reached the present Lao capital Vientiane in the evening.
A high-level business delegation, comprising of people from the Indian Chamber of Commerce in Laos, members as well as a 45-member business delegation drawn from FICCI, CII and ASSOCHAM which has flown in from India, called on the President at Vientiane to discuss their problems in doing business in Laos.
She assured them of all help, officials said. A joint high-level Indo-Laos business meeting will be held tomorrow.
President Patil will be accorded a ceremonial send-off soon thereafter by Laos and she will leave for Cambodian capital Phnom Penh to begin the second leg of her tour.
She will be in Cambodia till September 18.