Ajit Singh has urged the pilots to return to work, saying that their demands will be considered.
Thousands of passengers have been stranded and dozens of flights have been cancelled because of the strike.
The airline has sacked more than 70 pilots over the past few days in a dispute over training.
Mr Singh is expected to meet representatives of 13 recognised Air India unions at a meeting on Monday.
“It is more for familiarisation, to get to know them. Unions have a very important role to play not only about their demands but they should also look at the whole picture and health of their organisation,” he was quoted as saying by the Press Trust of India news agency.
The Indian Pilots Guild union, to which most of the striking pilots belong, has not been invited to the meeting, reports sat.
“The government has given money to Air India … They will have to understand what life is about in an era of competition,” Mr Singh said.