Addressing the Majlis-al-Shura or the Saudi Consultative Council here, he said India seeks a cooperative relationship with Pakistan for permanent peace as both countries are bound together by a shared future.
"We seek cooperative relations with Pakistan. Our objective is a permanent peace because we recognise that we are bound together by a shared future. If there is cooperation between India and Pakistan, vast opportunities will open up for trade, travel and development that will create prosperity in both countries and in South Asia as a whole," Singh said.
But to realise this vision, the Prime Minister asserted, Pakistan must "act decisively against terrorism".
"If Pakistan cooperates with India, there is no problem that we cannot solve and we can walk the extra mile to open a new chapter in relations between our two countries," Singh, who is on a three-day visit to the oil-rich kingdom, said.
Noting that both India and Saudi Arabia are threatened by extremism and violence, the Prime Minister said, "History teaches us that the scourge of terrorism must be confronted with determination and united effort.
"Nowhere is this challenge greater than in Afghanistan," Singh said.
"The people of Afghanistan have suffered for too long. They deserve an atmosphere of peace and the opportunity to pursue a life of dignity and hope," the Prime Minister said.
He said the pursuit of terror in the name of religion or any other cause or grievance cannot be acceptable to civilised societies. "It has no sanction in any religion."
Singh asked the international community to support all sections of Afghan society who wish to work towards the emergence of Afghanistan as a modern, stable and sovereign nation. "No sanctuary should be given to those who promote terror, violence or instability in the country."
He said India wishes to live in peace and friendship with its neighbours and that he believed that all countries of South Asia should work to realise a common vision of peace and inclusive development for the region.
Addressing the members of the legislative body that advises the Saudi King, Singh said Islam is an integral part of India's nationhood and ethos and of the rich tapestry of its culture. "India has made significant contributions to all aspects of Islamic civilisation. Centres of Islamic learning in India have made a seminal contribution to Islamic and Arab studies," he said.
"Our 160 million Muslims are contributing to our nation building efforts and have excelled in all walks of life. We are proud of our composite culture...," he said.
Returning to the issue of bilateral ties, he said India considers Saudi Arabia as a "pillar of stability" in the Gulf region and expressed confidence that the two countries could forge a "new partnership".
Describing west Asia as a vital part of India's extended neighbourhood, Singh said, "we have a high stake in the peace and stability of the region" and "neither the countries of the region nor the world could afford fresh turmoil."
He reaffirmed India's support for the struggle of Palestinian people and its backing for the Arab Peace Initiative to ensure peace and stability in the region.
Referring to his meeting with King Abdullah and other Saudi leaders on Sunday, Singh said these talks have led to reaffirmation of the close ties and common interests of the two countries.
"We have agreed to impart a strategic character to our relations, and have put in place a roadmap for bilateral economic, political and security-related cooperation that will constitute the core of our relationship in the coming years."
Singh said the kingdom is home to the largest Indian community abroad numbering 1.8 million and that Indian workers and professionals have participated in the "extraordinary development of this region".
He also expressed gratitude to Saudi Arabia for the warm welcome it has extended to the community as well as pilgrims from India who come here every year to perform Haj and Umrah.
"As many as 165,000 Indian pilgrims perform Haj annually...the second largest group from any single country," the Prime Minister noted.
He sought increased exchanges between parliamentarians, scholars, scientists and students of the two countries and observed that there is scope for considerable expansion of interactions in political, defence and security spheres.