The two leaders also agreed to enhance cooperation in defence and in international forums like the UN.
Morsi, who stressed on deeper economic ties, also pitched for increased Indian investment in Egypt's ambitious Suez Canal project.
"President Morsi and I have just concluded extensive and very productive discussions... We agreed that his visit, at an important juncture for Egypt, offers us a great opportunity to renew our relationship and take it to a different level of engagement and cooperation," Singh said after concluding talks with Morsi here.
"I am convinced that Egypt's successful transition would be an important model for the region and the world," he said.
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On his part, Morsi called Singh a "noble brother" and said his visit shows that Egypt is keen to cooperate with India.
The visiting dignitary also welcomed Indian companies' contribution in the nearly 200KM-long Suez Canal free trade zone project under which Egypt plans to turn the banks into a global economic zone.
Egypt should become the "hub of Indian exports to Africa", said Morsi who came to power after Egypt's first democratic elections last year that were held after the 30- year-old iron-clasp rule of former strongman Hosni Mubarak came to an end in February 2011 following a series of anti- regime protests known as Arab Spring.