The message comes a day after Indian Prime Minister Narendra Modi congratulated Sharif on the occasion of 69th Independence Day of Pakistan, which was celebrated on Friday. Both countries won independence from Britain on August 15, 1947.
"I would like to reiterate that promoting friendly, cooperative and good neighborly relations between our two countries is in our mutual interest and also necessary for peace and prosperity in South Asia," Sharif said in a message to Modi, as reported by Sputnik on Saturday.
"We in Pakistan sincerely hope to settle all our bilateral issues through a sustained and comprehensive dialogue and use a new era of mutual trust and cooperation," Sharif added.
There has been an escalation of tension between the two countries following renewed violence in the Indian-administered border region of Kashmir and Jammu despite a ceasefire agreement between India and Pakistan.
National security advisers from the both countries are scheduled to meet in New Delhi on August 23 to discuss terrorism-related issues.
The region of Jammu and Kashmir has been disputed by India and Pakistan following the dissolution of British India and the establishment of the two countries as independent states in 1947.