"I would like to reiterate that promoting friendly, cooperative and good neighbourly relations between our two countries is in our mutual interest," the prime minister said in his message.
"We in Pakistan sincerely hope to settle all our bilateral issues through a sustained and comprehensive dialogue and usher in a new era of mutual trust and cooperation," the High Commission of Pakistan in New Delhi tweeted citing Nawaz Sharif's message.
President Mamnoon Hussain said that "Pakistan remains committed to promote friendly relations between the countries for peace and prosperity in the region".
"It is our belief that cooperative relations between India and Pakistan will immensely benefit our two peoples," he added.
India celebrated its 69th Independence Day on Saturday, while Pakistan celebrated its Independence Day on August 14.