Yukio Hatoyama took office in September after 50 years of almost uninterrupted rule by the conservative, pro-US Liberal Democratic Party, but has since seen his popularity ratings slide to 50% in a survey published on Monday.
Both the countries have been working to improve ties since Japan had slapped sanctions on India in response to its 1998 nuclear tests.
Hatoyama launched his visit by meeting industrialists, including Tata group chairman Ratan Tata and Reliance Industries head Mukesh Ambani at a Mumbai hotel which was one of the targets attacked by gunmen in November 2008. He was due later to hold talks with Prime Minister Manmohan Singh.India, a top recipient of Japanese aid, wants details of Hatoyamas foreign policy, particularly Tokyos attempts to pursue a foreign policy more independent of Washington and improve ties with China, New Delhis longtime rival.
New Delhi will want to know more about Indias place in Hatoyamas proposed East Asian community with a single currency, inspired by the 27-nation European Union.
Trade, analysts say, is one way of cementing that partnership underscored by closer military ties and Japanese support for last years landmark US-India civilian nuclear deal.
The two sides...are in the process of concluding discussing a Comprehensive Economic Partnership Agreement (Cepa), said Indias foreign ministry spokesperson Vishnu Prakash. Twelve rounds of talks on the agreement had already taken place, he added.
Japan is Indias sixth largest investor. Bilateral trade, more than $12 billion in 2008-09, is expected to climb to $20 billion by next year.
Hatoyamas talks in India could also focus on climate change policieswith the two countries on opposite sides of the debate, particularly on expanding the scope of Japanese support for renewable energy projects in India.
Indian officials said they will also discuss Japans offer to train former Taliban fighters as part of a $5-billion Japanese aid package for Afghanistan. India remains uncomfortable about co-opting the Taliban into any power structures in Kabul.
Hatoyamas government will likely seek to present the visit as a success as domestic criticism rises. Last week he approved a record trillion dollar budget, which will further inflate Japans massive debt as the government struggles with the weak economy.
Japanese voters are also expressing growing doubts about Hatoyamas ability to make tough foreign policy decisions, and the arrest of two former aides has spurred calls for more explanation of a scandal over false political funding records.