"History has been created today. We have dared to reach out into the unknown. And have achieved the near impossible," said Modi, as India became the first country to succeed in the mission to Mars in its maiden attempt.
President Pranab Mukherjee and Vice President Hamid Ansari said the breakthrough will inspire the country's scientists to make even greater strides.
Congratulations poured in for the scientists from politicians, Bollywood celebrities and common people with many sitting in front of television early this morning to witness the historic moment.
In her message, Congress President Sonia Gandhi said that the achievement would be a source for inspiration "for generations to come" and commended the "courage, passion and imagination" of the team of space scientists and researchers led by ISRO Chairman Dr K Radhakrishnan.
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The US, China and Australia were among the countries which congratulated India after Mars Orbiter Mission (MOM) spacecraft 'Mangalyaan' slipped into a smooth orbit around the Red Planet after almost an year-long voyage.
"This is pride of India and Pride of Asia and also is a landmark progress in humankind's exploration of outer space. So we congratulate India on that," Chinese Foreign Ministry Spokesperson Hua Chunying said in Beijing.
US space agency NASA, which has just launched its own MAVEN mission to the Red Planet, also congratulated ISRO.
"The US Embassy congratulates India and the Indian Space Research Organisation on its Mars Orbiter Mission. India is in an elite group of space-faring nations by achieving insertion into Mars orbit," a statement from the US embassy here said.
"Mangalyaan... Bharat Mata ki Jai! Historic! Only country to have succeeded in first attempt, on budget less than Hollywood film... Our scientists have achieved what others could not... Badhai, Pyaar, Sneh, Abhinandan, aur Jai jai kaar! MOM (Mars Orbiter Mission)," Amitabh Bachchan, 71, posted on Twitter.