At a dinner hosted by Fehmida Mirza, the Speaker of Pakistan`s National Assembly or lower house of parliament, Kumar was repeatedly applauded by the gathering as she interspersed her speech with Urdu couplets.
Kumar praised the natural beauty of Pakistan and said: "Your matchless hospitality is famous in India. But after coming here, I have found that the hospitality, in reality, is even greater".
The parliaments of both countries, she said, have an important role to play in fostering better relations between the people.
The foundation of relations between India and Pakistan is based on common culture and links, including a shared love for music, films and sports, Kumar said. Indian film stars are loved in Pakistan, while Pakistani musicians and singers have huge followings in India, she added.
Referring to the passion for cricket in both countries, Kumar said more exchanges in all fields would help send a message of peace to the people.
"It is necessary for us to move towards the goal of friendship with greater speed," she said before concluding her speech with a couplet from Majrooh Sultanpuri.
In contrast, Mirza largely spoke in English and noted that the lower houses of parliament in Pakistan and India had women Speakers for the first time. Noting that this was a tribute to the women of the subcontinent, she said: "Women don`t make wars, women make peace. Women don`t take lives, women give lives". .
Mirza noted that she had visited India in a "tense atmosphere" in January 2010 to use parliamentary diplomacy to improve bilateral relations.
"During the last two years, the world community also witnessed a pleasant change as we both supported each other on numerous international parliamentary and other forums," she said.
She said that the two Speakers had identified several areas for cooperation during their talks earlier in the day.
"I am sure this process will yield positive results by not only breaking the existing myths but also in finding practical ways to solve the contentious issues affecting the growth of our mutual relationship," she added.
India-Pakistan relations have been marked by "missed chances and lost opportunities" and it was "now time to make up for the past", Mirza said.
The dinner was followed by performances by leading classical musicians and dancers. Among those who attended the event were Defence Minister Chaudhry Ahmed Mukhtar, Law Minister Maula Bux Chandio, former premier and PML-Q chief Chaudhry Shujaat Hussain, and scores of parliamentarians.