The President of Pakistan, Asif Ali Zardari, has held "friendly" talks with Indian Prime Minister Manmohan Singh on a rare visit to India.
"We would like to have better relations," Mr Zardari said after private talks with Mr Singh in Delhi.
The Indian leader said they shared a desire for "normal" relations between their countries.
It was the first visit to India by a Pakistani head of state in seven years. The two men last met in 2009 in Russia.
Mr Singh said he had accepted an invitation to visit Pakistan as soon as mutually acceptable dates were worked out.
Mr Zardari later departed for a visit to a Muslim shrine in Ajmer, 350km (220 miles) south-west of the Indian capital.
The shrine in Ajmer is dedicated to a Sufi saint, Moinudin Chishti, and is one of the most popular pilgrimage sites in the region, receiving a constant flow of devotees.
While the two leaders were meeting for lunch in private, a wide range of issues is said to have been discussed.
According to India's NDTV news channel, the two leaders agreed that their home secretaries would meet soon to discuss the issue of Hafiz Saeed, head of the Pakistan-based militant group Lashkar-e-Taiba.
Mr Saeed is accused of masterminding the 2008 militant attacks on Mumbai and Washington has announced a $10m (£6.3m) bounty for his arrest.
India says it has given Pakistan enough evidence to prosecute him but Pakistan says it needs "concrete evidence" before it can launch any legal proceedings.
India also reportedly offered to help Pakistan in its efforts to rescue dozens of people still buried under snow after a massive avalanche engulfed an army camp on the Siachen Glacier in the Himalayas.
Relations between the two countries have been gradually improving since peace talks were derailed after the Mumbai attacks.
Mr Zardari recently backed the lifting of trade restrictions on India, and Pakistan is also talking of dropping a restrictive list of what products it will buy from India.