Muktikant Biswal set out to walk from the eastern state of Orissa to the capital Delhi in the north.
He was hospitalised in Agra, 218km away from his destination.
Mr Biswal said he wanted to "remind" the prime minister of his promise to upgrade a hospital in his state.
He began his walk on 16 April with the Indian flag in hand, through increasingly worsening summer temperatures.
Mr Modi had said in 2015 that the hospital would be converted to a "super speciality facility" similar to the famed All India Institute of Medical Sciences in Delhi.
Mr Biswal told the BBC that he wanted to meet the Prime Minister and ask him to fulfil his promise of upgrading the Ispat General Hospital.
"I don't know whether the prime minister will meet me or not," Mr Biswal told the BBC. "If he doesn't meet me, I will go on a hunger strike."
Mr Modi has not reacted to Mr Biswal, whose story gained traction after this tweet by the leader of India's main opposition Congress party.
The PM promised Rourkela a multi speciality hospital three years ago. Now, Muktikant Biswal has walked 1,300 Km to Delhi because the PM hasn’t kept his promise & people are dying.
I assure Mr Biswal: the people of India & the Congress party will keep the PM’s promise for him.
Mr Biswal said he was glad that Mr Gandhi had tweeted about his walk and had promised to help, but he did not have details of how.
He is expected to arrive in Delhi later this week.
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