Cecil Chowdry, the Executive Director of the Catholic National Commission for Justice and Peace, also asked Christians to be praying for people in Pakistan, and for the heat wave to end.
He also said people living in the capital Karachi, and also remote villages, have been the most affected.
Temperatures in Pakistan have reached 45 degrees Celsius in recent days.
It has been reported power cuts across the main city, Karachi, mean people are unable to use air conditioning and fans to cool themselves.
The heat wave coincides with the Holy month of Ramadan, when most Muslims fast during daylight hours.
The government has encouraged people to stay at home and remain cool by declaring a holiday in the city.
Cecil Chowdry told Premier's News Hour: "It's very tragic. The government cannot seem to control the situation that is increasing day by day.
"Unfortunately this time in the big city of Karachi... [there's been] a lot of shortage of water and extreme humidity conditions."
"I think it's... important for the government to step up its efforts and to be ready for such situations. We have always faced heat waves in Pakistan and even worse than this; there was not enough preparation.
Listen to Premier's Marcus Jones speaking to Cecil Chowdry on the News Hour:
