"This is economic warfare," foreign ministry spokeswoman Lulwa al-Khater said at a press briefing.
Khater said the energy-rich emirate would "not leave a stone unturned" in legally pursuing claims for businesses.
Tensions have escalated in the Gulf since Saudi Arabia, the United Arab Emirates, Bahrain and Egypt cut all ties with Qatar in June, largely isolating the emirate in the oil-rich Gulf.
The four countries accuse Doha of supporting Islamist extremists and of being too close to Shiite Iran, Saudi Arabia's arch-rival.
More From This Section
Qatar denies the allegations, arguing the bloc aims to incite regime change in Doha.
The Gulf emirate says the sanctions have hit companies as well as citizens and expatriates.
It has set up a committee to pursue claims, which Doha says are potentially worth billions of dollars.