In the talks yesterday at the at the Al-Yamamah Palacehere yesterday, the King also appreciated India's interest in the Gulf as well as its keenness in supporting its stability of the countries in the region.
The King briefed the Prime Minister about Saudi Arabia's initiative to form a coalition to contain terrorism, Saudi officials said.
Oil-rich Saudi Arabia, a country known as spiritual home of Islam, has recently formed a major coalition of 34 Muslim nations to fight terror, particularly the ISIS.
The coalition includes nations with large and established armies such as Pakistan, Turkey and Egypt as well as war-torn countries with embattled militaries such as Libya and Yemen.
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Other members are Saudi Arabia's five partners in the Gulf Cooperation Council, as well as Jordan, Nigeria, Egypt, Chad, Mali, Malaysia, Morocco, Senegal, Somalia and Tunisia.
Saudi Arabia's regional rival, Iran, is not part of the coalition. Iraq and Syria whose forces are battling the Islamic State terror group are also not in the coalition.
The strong views by Saudi Arabia, known as spiritual home of Islam and one of the most influential country in the Gulf region, is seen asan unprecedented political endorsement of New Delhi's concerns about terrorism, extremism and radicalisation.
The two countries also signed an agreement in sharing intelligence related to money laundering and terror financing.
"We also stress the importance of continued cooperation and coordination with the government of your country in the field of counter-terrorism," the Saudi Foreign Ministry quoted the King as saying.
Reflecting growing congruence in ties, the two sides also
decided to ramp up defence cooperation including in maritime sphere and agreed to expand engagement in energy and infrastructure sector.
In the talks, the two leaders alsorejected totally any attempt to link terrorism to any particular race, religion or culture as they agreed to promote cooperation in cyber security, including prevention of use of cyber space for terrorism and radicalisation.
Its national daily Arab News had published a six-paged supplement on April 2, the day Modi arrived here, featuring articles relating to India-Saudi ties in diverse fields.
"King-Modi talks boost strategic partnership," said its headline on the front page about talks between the two leaders.