Koehler began the official leg of his week-long visit to India Tuesday with a ceremonial reception at the forecourt of the Rashtrapati Bhavan.
He arrived here Monday night on a multi-city tour, including New Delhi, Mumbai and Pune. It is the first visit by a German president to India in the last seven years.
The two leaders discussed proposed pacts on counter-terror cooperation and a framework agreement on economic and technological cooperation involving $500 million and decided to finalise them in the coming months.
The security pact envisages creating a legal basis and framework for the training of Indians by anti-terror specialists in Germany. The home ministry is examining a draft of the pact sent by German officials.
There was a meeting of minds between the two leaders with considerable expertise in economic issues on the global financial crisis and the need for sustained regulation of capital markets.
Manmohan Singh, an economist by training and a former governor of the Reserve Bank of India, is credited with opening India's overregulated economy in the 1990s when he was finance minister.
Koehler, a former head of the International Monetary Fund (IMF) and European Bank for Reconstruction and Development (EBRD), is well versed in issues of global financial governance.
The president backed the accommodation of major emerging economies like India in key global financial institutions.
Germany is India's biggest trade partner in the EU with bilateral trade estimated at over $20 billion.