They vowed to give a push to the bilateral relationship in all aspects and jointly deal with the common threats like terrorism.
"I remember what you told me in our first meeting - when it comes to India and Israel relations, the sky is the limit. But now, prime minister, let me add even sky is not the limit. We are also cooperating in space," Netanyahu told Modi.
Talking about the vast possibilities of cooperation between the two countries, he said, "We can do even more, even better together."
Speaking later, Modi said, "It is my honour to be the the first ever Indian prime to undertake this ground-breaking visit to Israel."
He said his visit was about the strength of the two societies and their strong partnership.
"Building a strong and resilient relationship with Israel will be my intent and focus...We have to secure our societies against the common threat of terrorism," Modi said.
"Together, we can do even more and even better (for India-Israel ties)," he added.
Noting that India is an old civilisation but a young nation, Modi said, "We have a talented and skilled youth, who are our driving force."
Describing Israel as an "important development partner", he said, "This is an exciting journey that we will undertake together, for the good of our people and our society."
Modi said his visit celebrates the strength of centuries-old links between the two societies and "based on these bonds, our partnership has maintained a strong and sustained upswing since the establishment of [the] full relationship, diplomatic relations, 25 years ago."
From the airport, Prime Minister Modi visited the Danziger flower farm in Moshav Mishmar Hashiva along with Netanyahu and Agriculture Minister Uri Ariel to learn about latest innovations and advancements in floriculture.
The farm, about 56 km from Jerusalem, is one of Israel's leading floriculture companies with approximately 80,000 square meters of state-of-the-art greenhouses specialising in the reproduction of plants.
"At the Danziger Flower Farm, advanced agriculture technologies were showcased by the Israeli Government," Office of the Prime Minister said in a tweet.
"The two leaders were briefed about the research technologies being used there for floriculture," the office said in a series of tweets.
The farm named a breed of chrysanthemum after Modi.
Modi also visited the Yad Vashem Memorial Museum to honour the memory of the victims of the holocaust that counts among the greatest tragedies in human history.
The museum occupies over 4,200 square metres — mainly underground — and emphasises the experiences of the individual victims through original artifacts, survivor testimonies and personal possessions.
The Holocaust was the killing of nearly six million Jews, including some 1.5 million children, by Adolf Hitler's Nazi Germany. Though the persecution of Jews began in 1933, the mass murder was committed during the more than four years of World War II.
Prime Minister Modi will have wide-ranging discussions on Wednesday with Netanyahu on the full spectrum of bilateral partnership and ways to strengthen it in diverse fields for mutual benefit. They will also have the chance to discuss major common challenges like terrorism.
Modi will meet President Reuven Ruvi Rivlin and address the chief executive officers (CEOs) of both the countries as well as the Indian diaspora on Wednesday.
He will also meet 26/11 Mumbai terror attack survivor Holtzberg Moshe, who was only two when he was saved by his Indian nanny Sandra Samuel. Moshe's father Rabbi Gavriel and mother Rivkah were among eight Israelis killed in the attack.
Modi will also pay his respects to the courageous Indian soldiers who laid down their lives during the liberation of Haifa in 1918.
During his visit to Israel, Modi will not travel to Ramallah, the seat of the Palestinian Authority, to meet with Palestinian leaders, as is common for visiting foreign dignitaries. He, however, said on the eve of his visit that India believes in a two-state solution in which both Israel and a future Palestinian state coexist peacefully.
India supports all efforts to find an acceptable solution to all the pending issues, including Jerusalem, he added.
The two-state solution envisions independent Israeli and Palestinian states coexisting side by side peacefully. This year, India and Israel are marking 25 years of their diplomatic relations.
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