Rivlin made a short speech before the Jewish community at the Taj Hotel in south Mumbai which was one of the places targeted by Pakistani terrorists.
He was accompanied by his wife Nechama, Maharashtra Governor C Vidyasagar Rao and protocol minister Ram Shinde.
"Nearly eight years ago, this wonderful city was the victim of one of the most terrifying, brutal and murderous terror attacks. Indians are no strangers to the threat and to the reality of modern global terrorism," Rivlin said.
"We cannot have adjusted to really rely on our values and words. And we must act and work together... Together to share intelligence and best practises to keep our people safe and to protect our brothers, our towns and cities. India and Israel stands shoulder to shoulder in this fight," he said.
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"We will fight terror, because this is a must for all free world," the visiting President said.
Without taking name, Rao said, "It is high time to recall that the terrorists receiving overt and coward support from the enemy nation targeted civilians and places like railway (station), hotels, cafeteria and community centres like Chhabad house (Jewish religious centre in south Mumbai)."
"We are grateful to Israel for standing by India and extending wholeheartedly support for its (India's) fight against terrorism," the Governor said.