The two sides discussed how to curb terrorism and facilitate people-to-people contacts, the official said.
The two countries have agreed to hold another round of peace talks on March 13-14, the Indian foreign minister and Khursheed Kasuri, his Pakistani counterpart, said.
Mukherjee also met Shaukat Aziz, the Pakistan prime minister, and invited him to attend a regional conference to be held in New Delhi in April.
Protest rallies
The arrival of Mukherjee triggered protest rallies among students in the Pakistan-administered part of Kashmir, the divided Himalayan territory at the core of the two countries' decades of rivalry.
Although the visit's main purpose is to invite Pakistan to New Delhi for this April's summit of the South Asian Association for Regional Co-operation, or Saarc, the two sides were also expected to discuss how to carry forward their peace process, begun in 2004.
Pakistan and India are main members of the Saarc, formed in 1985 to promote regional trade and economic cooperation.
The Saarc's members are Afghanistan, Bangladesh, Bhutan, India, the Maldives, Nepal, Pakistan and Sri Lanka.
Musharraf will skip it this summit and send Aziz.
Kashmir clash
Meanwhile, in Indian-administered Kashmir, two separatist fighters and a villager have been killed in a fierce gun battle with troops, an army spokesman said.
The firefight broke out on Saturday in northern Kashmir. "The exchange of fire [between separatists and soldiers] continues, a civilian also died in shooting," Lieutenant-Colonel AK Mathur, an Indian army spokesman, said.
The Muslim separatist revolt in the region has killed more than 45,000 people since 1989.