"I am sanguine that cricket matches between our two countries would prove to be a formidable confidence-building measure and a way forward towards encouraging people-to-people contacts," Zardari said in his letter.
"Undoubtedly, it would add to the positive atmosphere which has been witnessed by the two countries after resumption of the bilateral dialogue," Zardari said, referring to the Indian cricket boards decision this week to resume cricketing ties with Pakistan.
Zardari said he was "glad to learn that the cricket boards of Pakistan and India have agreed to resume cricket matches after a gap of five years".
A presidential spokesman said Zardari's letter was sent through the Pakistan High Commission in Delhi. The President recalled that he and Singh had discussed the resumption of cricketing ties between the two countries during his recent visit to India.
Zardari had met Singh when he made a private visit to India in April to offer prayers at a Sufi shrine in Ajmer. Zardari also conveyed his best wishes for Singh's health and the well-being of the people of India.
The Board of Control for Cricket in India has invited Pakistan to tour India for three ODIs and two T20 matches in December 2012-January 2013. The announcement has been welcomed by fans and cricketers on both sides of the border.
Cricketing ties between the two countries were suspended after the 2008 Mumbai attacks, which were blamed on the Pakistan-based Lashkar-e-Taiba. Pakistani authorities are yet to prosecute anyone for the attacks.
The two countries resumed their peace process last year after a gap of three years.