"We call on Israeli Prime Minister Naftali Bennett to impose an immediate moratorium on surveillance technology exports until a protective regulatory framework has been established," RSF head Christophe Deloire of the Paris-based group said in a statement.
His call came after a list was leaked of some 50,000 phone numbers believed to have been chosen by clients of Israel's NSO Group for possible surveillance, according to an international reporting effort.
The list contained numbers for 14 heads of state including French President Emmanuel Macron and Morocco's King Mohammed VI.
NSO's flagship program Pegasus can hack into mobile phones without users knowing, enabling clients to read every message, track a user's location and tap into the phone's camera and microphone.
NSO has contracts with 45 countries, and says Israel's defence ministry must approve its deals.
The company does not identify its customers. However, rights group Amnesty International and the Paris-based organisation Forbidden Stories that obtained the list said NSO's government clients include Bahrain, India, Mexico, Morocco, Rwanda and Saudi Arabia.
Reporting by media outlets including The Guardian, Le Monde and The Washington Post found that nearly 200 journalists from organisations including AFP were on the list.
"Enabling governments to install spyware that is used in practice to monitor hundreds of journalists and their sources throughout the world poses a major democratic problem," Deloire said.
Spokespeople for NSO, Bennett and Defence Minister Benny Gantz did not respond to questions from AFP on Wednesday.
NSO is a giant of Israeli tech with 850 employees.
Its CEO Shalev Hulio, 39, denied in an interview with Israel's 103FM radio on Tuesday that his company was engaged in mass surveillance.
He said NSO had "no connection" to the list of thousands of phone numbers.
On Wednesday, Bennett touted Israeli technological prowess at a cyber conference in Tel Aviv.
"Of every $100 invested in cyber defence across the world, $41 of those were invested in Israeli cyber defence firms," he said.
"We as a government, we as a nation, have to defend ourselves," Bennett added.
He suggested global interest in Israeli technology remained robust, saying "dozens of countries" signed memorandums to obtain Israeli tools that defend against cyber-attack.
On Tuesday, Gantz said Israel approves export of technology only to governments "exclusively for the purposes of preventing and investigating crime and terrorism".
He said Israel is "studying" recent publications on the subject.
