The PMO responded promptly and arranged help for Vaishali Yadav, who needed surgery for a hole in her heart, through the Pune district administration.
She was operated upon successfully early this month at a city hospital.
Vaishali on Saturday got the opportunity to meet Modi, who was in the city to launch projects under the Smart City mission. Pratap Yadav, her uncle, later told reporters that the PM offered her a chocolate and spoke to her a few sentences in Marathi.
The Prime Minister tweeted a photograph of his meeting with the little girl later.
"Priceless moments with young Vaishali", he said on Twitter. "After her surgery, Vaishali wrote a touching letter to me, which will remain etched in my memory...glad we were able to help this little girl," the Prime Minister said.