Shivshankar Menon, India's foreign secretary, said "both sides expect their business to increase".
But trade between Asia's largest and third-largest economies has so far failed to fulfil its full potential as Japan has focused on China and South-East Asia.
To help boost ties, the two sides will discuss a plan to build a $90bn industrial corridor with state-of-the-art infrastructure linking Delhi and Mumbai, India's financial capital.
The aim is to boost Indian manufacturing by making use of its cheap workforce while solving one of the bugbears of India's economy - its poor infrastructure and transportation.
Singh said efforts were under way to ensure a favourable climate in India to attract Japanese investment.
"In today's changed international system, the political, economic and strategic interests of India and Japan have never been so convergent," he said.
Indian government officials predict bilateral trade could double to around $14bn by 2012.
Besides economic ties, Abe and Singh were also so discuss ways to step up defence co-operation.
Japan and India are to join the US, Australia and Singapore in naval exercises scheduled to be held in the Bay of Bengal next month.
Also on the agenda were talks on civil nuclear co-operation with India hoping to tap into a global trade in civilian nuclear use, after a gap of three decades.
Earlier this month it revealed the details of an agreement with the US that requires the approval of a group that includes Japan.
Critics say allowing nuclear India - which is not a party to the Non-Proliferation Treaty - access to US nuclear technology and fuel would undermine global non-proliferation efforts.
On the environment, Abe is expected to seek co operation from India, one of the world's largest greenhouse gas emitters, in his so-called "Cool Earth 50" initiative aimed at halving global emissions by 2050 from current levels.
Abe will address a joint session of parliament during his three-day visit, a rare honour that officials tout as a sign of the importance of the visit.
Singh addressed the Japanese parliament on a visit to Tokyo at the end of last year