The two sides would try to take out the strain in their relationship developed over fuel subsidies last year.
This will be the King’s second visit to India in the past 12 months, and the first after the general elections in his country.
He will be the first foreign head to stay in the renovated Dwarka suite in the Rashtrapati Bhavan about two decades.
The King, who has come at the invitation of President Pranab Mukherjee, is accompanied by a high-level delegation comprising his Foreign Minister, Home Minister and Economic Affairs Minister.
Foreign Secretary and Army chief General Bikram Singh will call on him today, while tomorrow he will meet Prime Minister Manmohan Singh and the President. Besides, Vice-President Hamid Ansari, UPA chairperson Sonia Gandhi, Finance Minister P Chidambaram, External Affairs Minister Salman Khurshid, Home Minister Sushil Kumar Shinde, Leader of the Opposition in the Lok Sabha Sushma Swaraj and National Security Advisor Shiv Shankar Menon will call on him.
A controversy over suspension of subsidy to Bhutan on some petroleum products last year had become an issue in elections in which the then Prime Minister Jigme Thinley was defeated.