Patil, who arrived here yesterday on a six-day visit to China, was welcomed warmly by Wen at the Purple Light Pavilion.
Sources said Patil sought China's support for India's bid for a permanent seat in the United Nations Security Council. India has been seeking support from several countries for its bid for the permanent membership.
External Affairs Minister S M Krishna, who visited China last month, had also sought China's support in this regard.
Patil and Wen also discussed bilateral issues, particularly trade and commerce between the two countries.
Patil had yesterday indicated that she will raise the issue of India's bid for a permanent UNSC seat during her meetings with Chinese leadership and hoped that India will be considered for the membership.
China, which is one of the five veto-wielding members of the powerful UN Security Council along with the US, UK, Russia and France, has been saying that it supports India's aspirations to play an important role at the UN, but wants an overall reform of the world body.
Earlier, Wen warmly welcomed Patil and described her visit here as "significant" as it coincided with the 60th year of establishment of Sino-India diplomatic ties.
"It is a great pleasure to have you here. Let me welcome you to China. You are the first (Indian) President to visit in a decade," Wen said, while welcoming Patil.
The Chinese Premier said the visit is "significant" as it comes at a time when the two countries are commemorating the 60th year of establishment of diplomatic relations.
Referring to the India-style Buddhist temple in Loyang in central China, which Patil will inaugurate during her trip, Wen said this is yet another effort by the two countries to promote friendly relations.
In her remarks, Patil said: "I am very much pleased to visit you in China and I thank for the hospitality extended to me and my delegation. Excellent arrangements have been made for the visit and I thank you for that."
She also referred to Wen's last visit to India.
"We cherish your visit to India and remember your constructive role in building a strategic partnership between the two countries," she said. Patil will meet President Hu Jintao later in the day.
While Patil was assisted by Minister of State for Food Processing Subodh Kant Sahay, Foreign Secretary Nirupama Rao, Indian Ambassador S Jaishankar, the Chinese team included Foreign Minister Yang Jiechi and senior officials.
The President will meet her Chinese counterpart Hu Jintao later in the day. Hu will accord her a ceremonial welcome at the Great Hall of the People. However, chilly, damp weather led the President's office to move the ceremony from outside to indoors.
Later, Patil and Wu Bangguo, Chairman of the National People's Congress, met at the Great Hall of the People and discussed bilateral cooperation. Wu warmly welcomed the President and described her as an outstanding statesperson of India.
"It is a great pleasure to have you here. You are an oustanding statesperson of India. India and China have a strong relations and you continue to promote it," Wu told Patil. This is Patil's second visit to China. Earlier, she had been here in 1995 to attend an international conference.
Wu told Patil that he was happy to hear that she was visiting Loyang and Shanghai which will help her in better understanding of China. Patil said she was happy to visit China and that the country has undergone a "sea" and a "significant" change and development in the past 15 years.
"We appreciate this," she told Wu. She said apart from political impetus, the visit will help in bettering the bilateral ties. "You are also the architect of new China," she told the Chairman of the National People's Congress
