Al Jazeera America, the cable network that started 20 months ago to great fanfare and with big budgets, came under fire on Tuesday after the network was sued by a former employee and lost two executives.

Matthew Luke, formerly the network’s director of media and archive management, filed a lawsuit in New York Supreme Court claiming wrongful termination. Among other allegations, Mr. Luke said he was fired after he complained to the company’s human resources department about his boss, Osman Mahmud, who, Mr. Luke said, told him to exclude female employees from meetings and not involve them in projects that they had previously worked on.

In the suit, Mr. Luke asserted that Mr. Mahmud mistreated female employees and exhibited anti-Semitic behavior, including expressing a desire to replace an Israeli cameraman with a Palestinian. A female senior vice president who resisted fulfilling that request was later transferred to another position, the lawsuit says. The suit further claims that Mr. Mahmud said that “whoever supports Israel should die a fiery death in hell.”

Mr. Mahmud did not immediately respond to a request for comment. In an interview with The Washington Post, he denied making the comment about Israel, saying, “I have never even thought of that at all.” He called the accusations that he had mistreated women “a pack of lies.”