The leaders hope to strengthen ties between the two countries during the six-day visit, with deals on cybersecurity, energy, and space cooperation expected to be signed.
External Affairs Minister Sushma Swaraj met Netanyahu at the at Taj Diplomatic Enclave in New Delhi.
On Wednesday, PM Modi will accompany Netanyahu to Ahmedabad. Netanyahu will also visit Modi's home state of Gujarat in western India.
Ignoring New Delhi's stance on Jerusalem, Mr Netanyahu said he saw his visit to India as an "opportunity to cement cooperation with a world power in the areas of trade, security, technology, and tourism".
This is the first visit to India by an Israeli Prime Minister since Ariel Sharon came in 2003.
PM Narendra Modi and PM Netanyahu will be at the Teen Murti Memorial for a solemn ceremony. The Indian prime minister skipped Palestine during his trip leading many analysts to say that New Delhi was changing its rules of engagement in the region.More news: Terrifying false alarm scares over a million people in Hawaii
Of note, Israel will sign a cinema co-production agreement with India to strength ties between the two countries' film industries by granting joint government support funds for Israeli-Indian productions.
Daniel Carmon, the Israeli ambassador to India, played down India's vote. Last week, however, an Indian news agency reported that Delhi was considering the possibility of reviving the missile deal with Rafael.
The envoy also referred to the personal equation between Modi and Natenyahu.
"My wife and I stand here as a mother and father to a young son who loves the state of Israel with every fiber of his soul", he said of his 27-year-old son.
"You fight terrorism by fighting it", Netanyahu said.
"The relationship is an all-weather relationship", he told reporters Friday, adding it was "so strong and so important to both countries that our feeling is that nothing can reverse it".More news: MoneyGram partners with Ripple to increase payment speeds
A large delegation of 130 businessmen from 102 Israeli companies dealing with agriculture, water, cyber security, health care and security are companying with Netanyahu.
Carmon said 11-year Moshe Holtzberg will also accompany Netanyahu and participate in a function at the Chabad House in Mumbai.
"I don't think one vote affects a general trend you can see in many other votes and everything and these visits", Netanyahu said when asked to comment on India's vote at United Nations against U.S. decision to recognise Jerusalem as Israel's capital, in an interview to a TV news channel.
"I don't think it can influence the relationship".
India and Israel also do not see eye-to-eye on Iran, which New Delhi views as a strategic trading partner and gateway to Central Asia and Russian Federation.
Ties between the two countries have warmed considerably in recent years, especially since Modi took office.More news: Durant, Draymond shepherd Curry-less Dubs past Bucks
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