The Gupta family will on Friday morning file responding court papers at the High Court in Pretoria t.
In a Tweet published late Tuesday California time, CEO Dick Costolo said his company "is actively suspending accounts as we discover them related to this graphic imagery," and he gave a link to a New York Times story about Foley's killing.
Twitter spokesman Nu Wexler confirmed Costolo's Tweet and referred further questions to a company policy page. Twitter allows immediate family members of someone who dies to request image removals, although the company weighs public interest against privacy concerns.
Twitter users who oppose spreading the images are using the trending hashtag #ISISMediaBlackout.