Here are the latest developments:
PM Modi held talks with the head of the Ireland government, Taoiseach Enda Kenny and spoke about international challenges like terrorism. "I was pleased to exchange views on a broad range of international challenges, including terrorism, radicalisation and the situation in Europe and Asia," PM Modi said at a joint media event with Mr Kenny.
He later interacted with the Indian community in Dublin where he took a dig at the opposition back home. "Irish children are reciting Mantras, welcoming us. And it didn't feel like they were just reciting, it felt like they had 'internalized' the feeling behind them. If we would have done something like this (reciting mantras and welcoming a foreign dignitary) they would have raised questions on secularism," the PM said.
PM Modi is the first Indian Prime Minister to visit Ireland in almost 60 years. He was received at the airport in Dublin by the country's health minister Leo Varadkar and others. From Ireland, PM Modi left for New York.
In New York, PM Modi will attend and address some summits and will also attend a working dinner with CEOs of Fortune 500 companies to discuss investment opportunities in India.
On Saturday morning, just before he leaves for the West Coast, PM Modi will host German Chancellor Angela Merkel, Japanese PM Shinzo Abe and Brazilian President Dilma Rousseff at the Waldorf Astoria hotel in New York.
At that power-packed special summit of what is known as the G-4 group - countries which back each other's bid for permanent seats at the UN Security Council - the Prime Minister will push for a permanent seat for India on the UN Security Council.
From New York, the PM will travel to Silicon Valley where he will visit the Facebook headquarters in California for a Townhall with its CEO Mark Zuckerberg. He will also visit the Google campus and Tesla Motors.
He will also address the 'India-US Start-up Konnect', where Indian startups will present their products to an American gathering.
In San Jose on Sunday, September 27, PM Modi will interact with the Indian community at the SAP Centre, an event that the organisers say will be as grand as his reception at New York's Madison Square Garden last year.
The Prime Minister heads back to New York where he will meet US President Barack Obama in the last part of his six-day trip.
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