Koshiyari, who was in Kathmandu to attend the first meeting of the eminent persons group from India and Nepal, told the Himalayan television "it is up to the people of Nepal to decide whether they wanted Hindu Kingdom to be reinstalled in the country."
"India does not have any say about that," he said.
Nepal was converted into a secular state from a Hindu nation in 2008 through a Parliament declaration following the abolition of the 240-year-old monarchy from the country.
But they were ousted in 2013 in the constituent assembly polls.
According to official figures, over 81 per cent of Nepal's nearly 28 million people are Hindus, followed by 9 per cent Buddhists, 4.4 per cent Muslims and 1.4 per cent Christians.
In another interview to the BBC Nepali service, Koshiyar admitted that he met Nepal's deposed king Gyanendra Shah last month during a visit to the country.
Kosiyari said he met Shah in the third week of June.
"(Shah) is a citizen of this country and if someone wants to meet me, then it's my duty to meet that person," he said.
Koshiyari, however, said he has no plans to visit the former king this time.
Shah, the last king of the Shah dynasty, ruled Nepal from 2001 to 2008. He took charge of absolute power in February 2005 that lasted for 13 months.
The Shah dynasty rulers were revered as incarnations of Lord Vishnu and performed public rituals during festivals.
Koshyari is a frequent traveller to Nepal and enjoys good relations with senior politicians in Nepal.
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