Afghan President Hamid Karzai has sought to reassure Pakistan about a strategic partnership agreement he signed with India in Delhi on Tuesday.
"Pakistan is a twin brother, India is a great friend. The agreement that we signed yesterday with our friend will not affect our brother," he said.
India has promised to help Afghanistan when foreign forces withdraw in 2014.
Correspondents say the deal is viewed with suspicion in Pakistan, which sees Afghanistan as its backyard.
"This strategic partnership... is not directed against any country... this strategic partnership is to support Afghanistan," President Karzai said during a lecture organised by an Indian think-tank on Wednesday.
His two-day visit to India has been planned for months but it follows a series of attacks in recent weeks which have damaged ties between Kabul and India's rival, Pakistan.
India is a major player in Afghanistan and has already pledged $2bn (£1.3bn) in assistance.
At Tuesday's press conference in Delhi, Mr Singh said violence in Afghanistan was undermining security in South Asia.
He said that the strategic partnership between the two countries would create an "institutional framework" so that India could help in Afghan "capacity building" in the areas of education, development and people-to-people contacts.
The pact is believed to include an Indian commitment to increase its training of Afghan security forces, including the police, although Mr Singh made no reference to that in his press conference remarks.
The prime minister said that the two countries had also signed two agreements relating to Afghanistan's energy requirements which represented "a new dimension in economic relations" to enable Kabul to integrate more effectively with the Indian economy and other economies in South Asia.
He said that the people of India sympathised with Afghanistan as it sought to cope with "acts of terrorism... particularly the assassination of [peace envoy] Burhanuddin Rabbani".
"Rabbani was our guest in India in July and we were greatly encouraged by his vision," Mr Singh said.
"His brutal assassination should... strengthen our resolve to jointly confront the menace of terrorism."
President Karzai said that he was "grateful" for India's help and reiterated that his government would work closely with the US, Europe and India to plan Afghanistan's future.
Correspondents say Delhi is concerned about the security situation in both Afghanistan and Pakistan, particularly as foreign troops begin to withdraw from the region.
India is one of Afghanistan's biggest donors, having pledged money for projects ranging from road construction to the building of the Afghan parliament - and is keen to play a bigger role.
Delhi has often accused Islamabad of links to groups such as Lashkar-e-Taiba and the Haqqani network that have carried out attacks in Afghanistan on Indian targets, including an assault on the Indian embassy in Kabul in July 2008, in which 40 people were killed.
Last week, US officials demanded Pakistan stop supporting the Haqqani network, an allegation Islamabad rejects.