Responding to Khan's tweet, Modi said: "Thank you PM @ImranKhanPTI. I warmly express my gratitude for your good wishes. I have always given primacy to peace and development in our region."
Khan had sparked a political storm ahead of India's general polls by saying saying he sees a better chance of peace talks with India if Prime Minister Narendra Modi's BJP wins the national election.
He had said if the next government in India were to be formed by the Congress party, it might be "too scared" to seek a solution with Pakistan over Kashmir, fearing a backlash. "Perhaps if the BJP - a right-wing party - wins, some kind of settlement in Kashmir could be reached," Pak PM was quoted as saying by news agency Reuters.
Meanwhile, in his congratulatory message, Russian President Vladimir Putin expressed his wish to strengthen ties between the two countries.
"From a long standing friend! Russian President Putin has sent a congratulatory message to PM and has confirmed his readiness to work together to build the full range of bilateral relations and constructive interaction in international affairs," External Affairs Ministry spokesperson Raveesh Kumar said in a tweet.
Chinese President Xi Jinping in a letter to Modi noted the "great importance" he attached to the development of Sino-India relations and his desire to work with the Indian leader to take the development partnership between the two countries to a new height.
Xi said under the leadership of the two leaders, Sino-India ties have "shown strong momentum of development".
Sri Lankan President Maithripala Sirisena tweeted: "Congratulations on your victory and the peoples re-endorsement of your leadership. Sri Lanka looks forward to continuing the warm and constructive relationship with India."
The island country's Prime Minister Ranil Wickremesinghe also congratulated the Indian Prime Minister for his "magnificent victory".
Nepali Prime Minister K.P. Sharma Oli wished Modi "all success ahead" and said, "I look forward to working closely with you."
Afghanistan's President Ashraf Ghani tweeted: "The government and the people of Afghanistan look forward to expanding cooperation between our two democracies in pursuit of regional cooperation, peace and prosperity for all of South Asia."
Bangladesh Prime Minister Sheikh Hasina wished "peace, happiness and prosperity for the people of India".
Israeli Prime Minister Benjamin Netanyahu congratulated Modi and vowed to strengthen their "great friendship" as well as bilateral ties. "Heartfelt congratulations, my friend @Narendramodi, on your impressive victory in the elections," he tweeted in Hebrew.
"The election results are more validation of your leadership and the way you lead the largest democracy in the world. Together we will continue to strengthen the great friendship between us, and between India and Israel and take it to new heights," the Israeli leader said.
Maldivian President Ibrahim Mohamed Solih said it was "a strong affirmation of the Indian people's confidence in the BJP-led government. I look forward to closer and enhanced ties".
Japanese Prime Minister Shinzo Abe called Modi and both leaders reiterated their commitment towards strengthening the India-Japan special strategic and global partnership, said the Ministry spokesperson.
Bhutan, Vietnam and Portugal Prime Ministers Lotay Tshering, Nguyen Xuan Phuc and António Costa, respectively, as well as Tanzanian President John Magufuli extended their congratulations to the Indian leader and sought to boost bilateral relations.
Around 67 per cent of the nearly 900 million voters in India exercised their franchise in the seven-phased elections that began on April 11 and ended on May 19.
(With additional information from IANS)