"The President of Israel welcomed me so warmly, he broke protocol. This is a mark of respect for the people of India,"Modi tweeted.
Modi, who arrived in Tel Aviv yesterday for a three-day visit, met Rivlin at his residence here and thanked him for the "warm hospitality and friendship".
"It is a privilege to meet President Rivlin again today. I fondly recall his visit to India last November when he charmed us with his affable manner and desire to do more with India," Modi wrote in the guest book at the Presdient's residence.
"President Rivlin is admired in India for his unstinting belief and common good of mankind, I thank him for his friendship and his warm hospitality," wrote Modi, who is the first India prime minister to visit Israel.
Here are five things that define the India-Israel relationship:
Defence: India is Israel's top destination for arms exports, buying 41 per cent of export between 2012 and 2016, according to the Stockholm International Peace Research Institute, an independent global conflict and arms-research institute.
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Israel is India's third-largest source of arms, with a 7.2 per cent share of imports between 2012 and 2016, next to the US (14 per cent) and Russia (68 per cent).
The earliest signs of collaboration came during the 1962 Sino-Indian war, when Israel provided India military aid. Israel also assisted India during two wars with Pakistan in 1965 and 1971.
India reciprocated during the six-day war in 1967 by providing Israel with spare parts for French-made Mystere and Ouragan aircraft as well as AX-13 tanks (also French-made).
The highlight of the partnership was Israel's supply of artillery shells during the Kargil war in 1999 when India faced a shortage.
In the late 1990s, a crucial defence deal was the Indian purchase of Barak 1, an air-defence missile, bought specifically for its capability to intercept US-made Harpoon missiles deployed by Pakistan.
India's imports of unarmed aerial vehicles (UAVs) have almost all been from Israel. Of 176 UAVs purchased from Israel, 108 are Searcher UAVs and 68 are Heron UAVs.
In April 2017, India and Israel signed a $2 billion deal for an advanced medium-range surface-to-air missile system, which will provide the Indian army the capability to shoot down aircraft, missiles and drones at ranges of up to 70 km.
In September 2016, tests were conducted of the jointly developed Long Range Surface-to-Air Missile with a range of 70 km, intended to equip three guided-missile destroyers of the Indian Navy.
India successfully tested the Israeli-made SPYDER quick-reaction surface-to-air missile in May this year. The Indian Air Force (IAF) is planning to deploy this system on its western border.
India and Israel also closely cooperate on counter-terrorism issues through a joint working group on counter-terrorism.
Diplomacy: Several ministerial and high-level official visits to Israel preceded Modi's tour. These included visits by then Home Minister L.K. Advani in 2000, former President A.P.J. Abdul Kalam in 2008, Home Minister Rajnath Singh in 2014, President Pranab Mukherjee in 2015 and External Affairs Minister Sushma Swaraj in 2016.
Three Indian naval ships, destroyer INS Mumbai, frigate INS Trishul and tanker INS Aditya, made a goodwill visit at the Haifa port in May 2017 to mark 25 years of full diplomatic relations between the two countries.
Agriculture: An Indo-Israel agriculture action plan for 2015-18 is operational, and 15 of the proposed 26 centres of excellence in agriculture are being developed in India with Israel's help to showcase the latest technology to Indian farmers.
Phase-I (2010-12) and phase-II (2012-15) of the agreement are complete, according to a reply to the Lok Sabha.
India has benefited from Israeli technologies in horticulture mechanisation, protected cultivation, orchard and canopy management, nursery management, micro-irrigation and post-harvest management, particularly in Haryana and Maharashtra.
Every year, more than 20,000 farmers visit the Agricultural Centre of Excellence at Gharaunda in Karnal, Haryana, where a nursery produces hybrid seedlings -- including tomatoes, cherry-tomato, colored capsicum, cucumbers, eggplant and chilli pepper-grown in small, individual cells, ready to be transplanted into containers or a field.
There was a five-to 10-fold increase in crop yields with an accompanying 65 per cent reduction in use of water and noticeable decrease in the use of pesticides and fertilisers, according to a December 2014 report on the Indo-Israel Agriculture Project.
Water Management: On June 28, 2017, the Union cabinet approved a memorandum of understanding (MoU) with Israel on the National Campaign for Water Conservation in India.
Technologically-adept Israel has developed water-management technologies, located as it is in a semi-arid region with limited sources of fresh drinking water.
India and Israel had earlier signed an MoU on water resources management and development cooperation in November 2016.
Trade: Israel was India's 38th-largest trading partner, with trade of $5.02 billion (Rs 33,634 crore) in 2016-17, down 18 per cent over 2012-13. The trade balance stood in India's favour at $1.10 billion (Rs 7,370 crore) in 2016-17.
Mineral fuels and oils are India's leading export to Israel, worth $1.01 billion in 2016-17.
India's major imports from Israel in 2016-17 included natural or cultured pearls and precious stones, worth $1.11 billion.
Trade in diamonds accounts for nearly 54 per cent of the bilateral trade. Nearly 40 diamond dealers from India have opened offices at the Israeli diamond exchange in Ramat-Gan. Some of these dealers have been active in Israel for nearly 30-40 years.
The Israeli government has proposed measures such as "offering export insurance, liberalising the aviation sector and granting longer-term visas". The aim is to boost Israeli exports to India by 25 per cent over the next four years and tourists to 80,000 annually.
"Relations with Israel are significant for India because of cooperation in agriculture, defence and science/technology," Uttara Sahasrabuddhe, professor of international relations at the University of Mumbai, told IndiaSpend.
"Israel has been giving key weapons systems to India, including missiles; it has given us those weapons which we could not directly buy from the US for ideological reasons; cooperation in counter-terrorism from information sharing to techniques/doctrine of counter terrorism," Sahasrabudde said. "It is also an important source of foreign investment, if tapped with care. The visit of the Indian PM will indicate that New Delhi has come out of the old mindset."
(With inputs from agencies)