In a letter sent to Singh, Ashraf said: "Your kind thoughts and expression of solidarity with the families of the victims and the people of Pakistan in this hour of grief are indeed a source of great strength and solace for us."
Earlier, Singh sent a condolence message to Ashraf and expressed his sorrow at the tragic loss of lives in the fires in two factories in Lahore and Karachi.
"I was deeply saddened to learn of the loss of lives in the fire accidents in Karachi and Lahore on Tuesday, September 11," Singh said.
"On behalf of the government and the people of India, and on my own behalf, I convey our deepest condolences to the families of the victims of the two tragedies. May the Almighty give the bereaved the strength to withstand this irreparable loss," Singh said.
Nearly 300 people were killed and dozens more injured in the two fires.