The list of 72 most-powerful people in the world also included Reliance Industries Ltd (RIL) Chairman Mukesh Ambani at 36th, ArcelorMittal Chairman and Chief Executive Officer (CEO) Lakshmi Mittal at 57th, and Microsoft India-born CEO Satya Nadella at 64th.
On Modi, Forbes said "India's newest rock star doesn't hail from Bollywood. He is the newly elected Prime Minister who sailed into office in May with a landslide victory, ushering the Bharatiya Janata Party into power after decades of control by the Gandhi dynasty." Forbes described him a "Hindu nationalist" and referred to the 2002 Gujarat riots when he was the state's chief minister.
"Modi is credited with massive reconstruction projects in his home state of Gujarat. His administration promises to bring economic rejuvenation to other beleaguered parts of India. The world is as impressed as the citizens of India: So far he's toured the US and China and met with his Southeast Asian neighbours," the magazine said.
This year there are 12 newcomers on the list, including Modi and Egypt President Abdel el-Sisi.
Alibaba founder and China's richest man Jack Ma also makes a first appearance on the list after his record-breaking $25-billion Initial Public Offering in September, as does terrorist group Islamic State's chief Abu Bakr al-Baghdadi.
An omission from the list was Congress Party President Sonia Gandhi, who was the highest-ranked Indian last year at 21, and the third most powerful among women.
The next Indian after Modi on the list is Ambani at 36th.
Forbes said Ambani had business ventures in petrochemicals, manufacturing, oil and gas production, and now wireless sectors, "the sum of which have landed him as the richest person in India for eight years running." It noted RIL's $655-million acquisition of media outfit Network18.
In October, Modi had inaugurated Ambani's Reliance Foundation's new hospital in Mumbai, "ending rumours about Ambani's waning clout in New Delhi," it said.
This is the second year Putin carries the crown. Obama had topped the list every year, with the exception of 2010, when Hu Jintao, the former President of China, was ranked one.
The top five remain the same as 2013 -- Chinese President Xi Jinping ranked third, Pope Francis at number four and the world's most powerful woman German Chancellor Angela Merkel ranked fifth.
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