"We have historic relations with each other. There is a strong link of Buddhism. Those monks who come to study here...Are very happy. I understand it will give a cordial atmosphere to further our relationship," she underlined.
The Buddhist monks were earlier given one year visa and they had to return to their country and come back again with a new entry permit in case the duration of the course was more than 12 months.
Patil, who was on a week-long tour of South Korea and Mongolia to boost India's 'Look East policy' and strengthen trade and security related ties, met her Korean counterpart Lee Myung-bak and Mongolian President Tsakhia Elbegdorj.
Besides, Seoul and Ulaanbatar also agreed for direct air links with New Delhi.
"People of both the nations and government wants to further their relation and therefore we decided to have direct links... Both the nations have agreed upon it," Patil said.
India also inked a nuclear pact with South Korea for peaceful uses of atomic energy and another agreement on cooperation in defence with Mongolia.
"We will work with South Korea and move forward to strengthen bilateral ties. There is going to be a conference on nuclear conference in South Korea and India will participate in that," Patil said.
"So far Mongolia is concerned, we already have a MoU with them in civil nuclear cooperation," she said, adding that a team from Mongolia will soon come to India for further discussion in this regards.
The President said as "nuclear energy is very important to India", New Delhi underlined the need to further the economic partnership.
"Mongolia is mineral rich country especially in steel and uranium. I have impressed upon (their) leadership that it is for mutual benefit that we move together," Patil pointed out.
India has also signed a MoU on media exchanges with the two nations.
She said during the "friendly and productive" meetings with the presidents and other leaders of both the nations, "there was a clear desire to expand and deepen relations with India."
"I fully reciprocated these sentiments and indicated that we wanted to take our strategic partnership with the Republic of Korea and our comprehensive partnership with Mongolia to a higher trajectory," the President underlined.
"President Lee and I agreed to enhance defence and security cooperation between our two countries including naval cooperation to protect the sea lanes of communication," she said.