Sinn Féin MEP Lynn Boylan has written to Ireland's EU Commissioner Michael McGrath expressing concern that EU citizens whose data is processed in Israel may not have their rights protected under the General Data Protection Regulation (GDPR).
Under EU rules, Israel is among a number of third countries who do not require specific authorisation for data transfers under the GDPR.
In January, the European Commission confirmed that Israel was one of 11 countries outside the EU that continued to enjoy the adequacy status that was rolled over from the original legislation, the 1995 Data Protection Directive.
In the letter, Ms Boylan challenges whether Israel should avail of such a privilege because there were "significant concerns" that the rights of EU citizens under the GDPR, whose data was processed in Israel, would not be protected.
Specifically, the Dublin MEP said that Israeli authorities had not provided information to EU citizens who may have been affected by surveillance operations involving so-called Pegasus spyware, operated by the global cyber-intelligence company NSO Group.
"EU citizens affected by the targeted surveillance operations involving NSO Group's Pegasus spyware have not been afforded this right with requests to the Israeli authorities for information on NSO Group clients gone unanswered," the MEP writes.

The use by Israel of Pegasus spyware was highlighted in a report by a special committee of the European Parliament.
Ms Boylan said the "lack of meaningful dispute resolution processes where EU citizens' personal data is incorrectly processed raises serious questions regarding the adequacy status enjoyed by Israel".
The European Commission report on data adequacy in Israel and ten other countries in January noted that the EU had adopted a decision in 2011 granting Israel adequacy status.
The reports said that since then "Israel's framework for the protection of privacy and personal data has been significantly strengthened through a number of developments at legislative, regulatory and enforcement level".
However, in her letter, Ms Boylan said that it has "long been established that the Israeli government carries out intense surveillance of the civilian population of the occupied Palestinian territories - including biometric surveillance such as facial recognition technology in order to maintain the illegal occupation".
She said that the GDPR required the commission to take into account criteria such as respect for the rule of law, access to justice and international human rights norms and standards when granting data adequacy status.
Mr McGrath, who was confirmed as the EU's Justice Commissioner in November, covers the GDPR as part of his portfolio.
RTÉ News understands that the European Commission is preparing a response to Ms Boylan's letter.