The European People's Party (EPP) group voted against the report in parliament's civil liberties, justice and home affairs (LIBE) committee, dismissing most of its content as "plain absurd and nonsense".
The report, however, was passed on Thursday and is due to go before parliament's Strasbourg plenary session in September.
EPP group shadow rapporteur Elissavet Vozemberg said, "Fundamental rights are the foundation on which the EU is built. For the EPP group, fundamental rights should be continuously protected and strengthened, as this is the most efficient way in order for the rule of law and democracy to be properly safeguarded and implemented.
The EPP were particularly critical of a compromise amendment in the report which calls on member states to guarantee that national law only permits the collection and investigation of personal data where the individual concerned has provided consent.
"Unfortunately, it is disquieting to see that the coalition of far-Left, Left and Greens is wrongly using this report to promote the protection of criminals and terrorists," said Vozemberg.
EPP group coordinator in LIBE Monika Hohlmeier also slammed the committee's decision, saying, "It is unbelievable that the Socialists, Liberals, Greens and Communists are using fundamental rights to protect criminals and terrorists.
"They want to inform terrorists who are being chased by police in order to protect their fundamental rights and personal data. They see fundamental rights being threatened by bad quality media and are asking the commission to interfere with press freedom," she added.
The Progressive Alliance of Socialists and Democrats (S&D) group shadow rapporteur Péter Niedermüller, however, stressed that member states must be held to their commitments on fundamental rights.
"A big problem we face in the EU is that after countries have become members, we have no viable means to enforce their continued commitments to the European values enshrined in the treaties, like the rule of law and respect for fundamental rights," said the Hungarian deputy.
Citing the need for "mutual trust" between member states, he said the S&D are proposing "a new mechanism that is designed to monitor and remedy the breaches to avoid systematic threats".
"The EPP group voted against this idea, perhaps they are worried that some of their national governments would not withstand such scrutiny."
The 'grand coalition' between parliament's 221 EPP deputies and 191 S&D gives the two groups a majority of 412 of the total 751 MEPs. Ad hoc alliances are often formed among parliament's political groups, but the coalition is intended to provide a stable majority across a number of policy areas.