Both sides also supported each other's claims for permanent membership of the United Nations Security Council.
The Addis Ababa Declaration adopted at the end of the second Africa-India Forum Summit here also called on all countries to ensure that acts of cross-border terrorism do not occur and that their territories are not made a base for terrorists.
"We unequivocally condemn terrorism in all its forms and manifestations. An act of terrorism anywhere is a threat to the entire international community," the Declaration said.
"We recognise the need to further strengthen international cooperation to combat global terrorism and for compliance of all member states with all international terrorism conventions and related protocols and United Nations Security Council's resolution on counter-terrorism," it added.
The summit was co-chaired by Prime Minister Manmohan Singh and and Equatorial Guinea President Obiang Nguema Mdasogo.
The declaration called on all states to cooperate with each other in prosecuting, extraditing and rendering legal assistance with regard to actions of international terrorism.
The leaders deplored the tragic loss from terror attacks and called for the active prosecution of the authors of such crime and their accomplices and urged that they be brought to justice expeditiously.
Taking on board serious concerns over the problem of piracy, the leaders strongly condemned kidnapping and hostage taking as well as demand for ransom and political concessions by terrorists groups.
"We express serious concern at the increase in such incidents," the Declaration said.
India has voiced its serious concerns over the threats posed by Somali pirates since about 11 per cent of seafarers engaged by international shipping companies are Indian nationals, some of whom have been taken hostage.
There have been over 200 attacks, including about 70 successful hijackings and ransoms believed to exceed USD 50 have been paid to the pirates for securing the release of hostages and ships.
Taking note of the African position on the condemnation of the payments of ransom to terror groups, they (leaders) called for the urgent need to address the issue.
The two sides underscored the imperative need for urgent and comprehensive reforms of the UN systems which must reflect "contemporary realities".
India supports Africa's claims for permanent membership of Security Council. On its part Africa backs India's claim to a permanent seat with full rights in an expanded security council.