Talks between India and China have led to a major improvement in relations, following a landmark agreement over the status of Tibet.
Mr Vajpayee with former Chinese President, Jiang Zemin
India has now formally recognised that the area known as the Tibetan autonomous region is part of the People's Republic of China.
China, for its part, has agreed to start border trade through the north-east Indian state of Sikkim - a move that is being seen as an acceptance by Beijing of India's claim over that area.
Indian Prime Minister Atal Behari Vajpayee says relations with China have been transformed as the two sides seek new ways to overcome their differences.
However, BBC India correspondent Sanjeev Srivastava says the joint declaration is in reality as much diplomatic fudging as genuine progress in areas of differences.
The Tibet and Sikkim agreements are the first details to emerge of a declaration signed by India and China aimed at solving their long-running border disputes, which erupted into war in 1962.
Mr Vajpayee is on the second full day of what is the first visit to China by an Indian prime minister for 10 years.
"Our present course of developing all-round bilateral co-operation, while simultaneously addressing our differences, has transformed the quality of our relationship," Mr Vajpayee said on Tuesday.
He was speaking after talks with former Chinese President, Jiang Zemin.
The world's two most populous nations have appointed envoys "to explore from the political perspective of the overall bilateral relationship the framework of a boundary settlement", according to a joint declaration released after the talks.
Mr Vajpayee added: "The appointment of special envoys is a special step that reflects the desire of both countries to settle the border issue as early as possible."
The joint declaration adds that India will not allow "anti-China political activities" by Tibetan exiles, who have fled to India in their tens of thousands.
The Indian Foreign Minister has said this will not affect the status of the Buddhist Dalai Lama,
who leads a Tibetan government-in-exile based in the Indian town of Dharamsala.
The agreement has surprised observers as border disputes have bedevilled relations between China and India.
Fifteen rounds of talks since the 1980s have failed to resolve India and China's boundary disagreements.
Even in this declaration, our India correspondent says, the Indian leadership is keen to differentiate between the Tibet autonomous region and the whole of Tibet.
The Dalai Lama leads a Tibetan government-in-exile based in India
The Tibet autonomous region, west of the Yangtse river and south of the Kunlun mountains is the only area recognised by modern-day China as "Tibet".
It is about one third of the size of the old Tibet that existed before China invaded in 1950 and started incorporating areas into surrounding Chinese provinces.
Tibetan exiles in India believe improved relations between India and China would help
negotiations between the Dalai Lama and Beijing over Tibet.
Thubten Samphel, a spokesman for the
Tibetan government-in-exile, told
the Reuters news agency: "Relations between India and China based on mutual trust will enable India to play the role of a honest mediator to help resolve the Tibet issue."
The Dalai Lama wants to see greater autonomy for Tibet inside China's borders.
But Beijing usually accuses him of seeking outright independence for Tibet.
The Dalai Lama's London representative, Kesang Y Takla, described India's position as "not new... but it is certainly of interest and concern to all three parties concerned".
The director of the Tibet Information Network, Thierry Dodin, said local people living on the border would benefit from the establishment of Himalayan border trading posts.
in Sikkim and Tibet.
"Trade is something both nations see as being in their national interests," he told BBC News Online.
"The local population will benefit from that and both nations will benefit from that. In terms of the economy, tourism and communication it's a very important thing."
On Monday, Mr Vajpayee and Chinese Prime Minister Wen Jiabao signed nine agreements to boost relations between the two Asian rivals.
The agreements include:
- Increasing co-operation in science, technology, commerce and education
- Easing visa rules
- Setting up joint infrastructure development projects, focusing on water and energy resources
- Establishing cultural centres in each others' countries