"We will not bow down to terror," the National Association of Software and Service Companies (Nasscom) said in a statement.
"As an industry that is international and services customers across the globe, we continue our operations, uninterrupted, from centers across India and even Mumbai," said Nasscom.
The group said Indian outsourcers in the area are taking precautions "to ensure the safety and security of our employees, facilities, and visitors."
A number of major IT outsourcing companies, including Wipro, Infosys and TCS, maintain offices in Mumbai. The city also hosts offices for U.S. service providers such as IBM, HP, EDS, and Computer Sciences Corp.
Virtually all major Fortune 500 companies are dependent to some extent on IT services and software development sourced from India, which boasts a highly skilled technology workforce and low costs. The country exported more than $30 billion worth of software and related services last year, with exports growing about 25% per year.
Islamic terrorists attacked hotels and other public areas in Mumbai Wednesday, killing more than 100 people, including some foreigners, according to Reuters and other news agencies. One terrorist who spoke to an Indian television station said the attacks were meant to draw attention to the treatment of Muslims in Kashmir, a disputed region claimed by both India and Pakistan.
Nasscom called the attacks "dastardly" and said they were "clearly an act of terror designed to create fear and panic."
The group said its member companies are communicating with customers to keep them updated on the situation. It also said its own offices in the region are open and that all scheduled events will go on as planned.