Heads of government of Britain, Pakistan, Bangladesh, Sri Lanka, Afghanistan, Australia and Israel sent congratulatory messages to Mr Modi as the results were declared.
British Prime Minister called up and conveyed his greetings to Narendra Modi.
"The prime minister called Narendra Modi this morning to congratulate him on his victory in the Indian elections and the record turnout, making this the biggest democratic election in history," a Downing Street spokesperson said.
"Mr Modi said he would be delighted to accept the Prime Minister's invitation to visit the UK. Both leaders agreed on the importance of the UK-India relationship and agreed to work together to strengthen it in the months ahead."
Cameron also used his Twitter handle to convey his greetings.
"Congratulations @narendramodi on victory in India's elections. Keen to work together to get the most from UK-India relationship," Cameron tweeted in his official 10, Downing Street, account.
British Foreign Minister William Hague said Britain congratulates Mr Modi and the Bharatiya Janata Party (BJP) on their success in the elections.
"I congratulate Narendra Modi and the BJP on their success and look forward to forging an even closer partnership with India in the months ahead," Hague said in a statement.
"UK has strong ties with India and the British government looks forward to working with the new Indian government to build on this relationship and deliver security, growth and prosperity for both our nations."
Pakistan Prime Minister Nawaz Sharif too on Friday congratulated Mr Modi for winning the Indian general election.
Sharif telephoned Mr Modi and expressed his best wishes, Radio Pakistan reported.
Stating that he had followed the general elections closely, he also invited Mr Modi to visit Pakistan.
Afghan President Hamid Karzai also congratulated Mr Modi for leading the BJP to victory.
"President #Karzai extends his warm Congratulations to @narendramodi on victory in elections. Afghans always regard #India as a true friend," Aimal Faizi, spokesperson to the president, tweeted Friday.
Bangladesh Prime Minister Sheikh Hasina congratulated BJP president Rajnath Singh and Narendra Modi for the party's landslide victory in the elections.
"On behalf of Bangladesh Awami League (BNP) and my own behalf, it gives me great pleasure in heartily congratulating you and the members of your party on your landslide victory," Hasina said in her letter to Rajnath.
"The magnitude of victory is clearly reflective of the charismatic leadership quality of yours and the prime ministerial candidate Narendra Modi, your top office bearers and election campaign strategists and managers, as well as the huge degree of trust and confidence that the people of India have chosen to repose in your party and in your leadership," the statement said.
"I would like to take this opportunity to reassure you of my personal and my party's firm commitment to working with you and your party, and the elected government of India to bring about meaningful, tangible and positive changes in our close and friendly relations that would benefit our two great democracy-loving peoples," she said in her letter to Narendra Modi.
Her statement also praised Atal Bihari Vajpayee for his visionary leadership.
"The historic relationship between our two parties dates back decades," she said.
"The people of Bangladesh were thankful for the unprecedented degree of support and all-round assistance extended by the people of India to us during our Liberation War," she added.
Sri Lankan President Mahinda Rajapaksa issued an invitation to Mr Modi to visit Sri Lanka after the BJP's victory.
Presidential spokesman Mohan Samaranayake said that the president issued the invitation to Mr Modi after congratulating him on the election victory.
Australian Prime Minister Tony Abbott too called up Mr Modi to congratulate him for leading the BJP to victory.
"I've spoken to @narendramodi and congratulated him on his success. I look forward to strengthening ties between India and Australia," Abbott tweeted Friday in his official PM account.
According to Radio Australia, Abbott has invited Mr Modi to visit Australia for the G20 Summit to be held in Brisbane in November.
Prime Minister of Israel Benjamin Netanyahu also called Mr Modi and congratulated him on his victory.
"He (Netanyahu) said that he was looking forward to work with Mr Modi and enhance bilateral cooperation," a statement issued by the Gujarat Bhavan in New Delhi said.
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