Speaking on Thursday, Claude Moraes, the Chair of Parliament's civil liberties, justice and home affairs committee, said the recent terrorist atrocities in Barcelona and Finland "graphically highlight" the need for such action.
He was speaking after EU security policies were debated by the civil liberties committee.
MEPs discussed the comprehensive security assessment with European security union Commissioner Julian King at the committee meeting.
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The comprehensive security assessment reviews the EU's policies and instruments in the area of internal security over the last 15 years to see whether the activities are appropriate and effective and to identify any gaps requiring further action.
The report also provides an update on progress made in the implementation of legislative files on security, with the next steps taken to prevent terrorist financing through trafficking in cultural goods and to enhance the exchange of information.
It outlines efforts to prevent radicalisation online, strengthen the protection of 'soft' targets and support national action through EU funding for internal security policies.
After the presentation of the assessment and a debate in the committee, Moraes, a Socialist member, told this website, "Member states need to urgently implement the powers they already have in this area.
"The serious terrorist attacks this summer have demonstrated to us yet again the need to significantly reinforce security within the EU. This comprehensive assessment provided by the Commission responds to our request in the civil liberties committee for a thorough review of the EU's security policy to address any challenges and gaps in existing policy in the security field."
He added, "The EU is doing its job in this area, for example, delivering legislation on Passenger Name Records (PNR) and Europol but, ultimately, implementation of such policies is a competence for member states.
"The conclusions of the comprehensive security assessment show that important progress has been made, but they also highlight key areas where more action is needed, such as ensuring full implementation of existing legislation by member states and better use of information already available."
The MEP added, "Parliament will continue to engage with both the Commission and Council to ensure that particular attention is given to those instruments that have not performed as expected, and that the assessment's findings are acted upon.
Moraes said, "What is particularly needed is better intelligence sharing between member states. This is absolutely critical in the ongoing fight against terrorism and the new, emerging threats to our security in Europe such as those we recently saw in Barcelona.
"There is no room for complacency and the security assessment provided today by Julian King was very much welcomed by the committee as being a good start.
"This shows that good work is being done but it is also clear that a lot more still needs to be done."
Further comment came from King, who told the committee, "Overall, the review shows that member states now clearly recognise that the EU can and should play an active role on security. And there has been a step change in member states' engagement at the European level."
The British official went on, "Much has changed over the last decade: how the terrorists operate, and the tools at our disposal. It was right to do this review of our security policies."
The comprehensive assessment was promised by the Commissioner at his initial hearing before the civil liberties committee in September 2016 and the report was published by the Commission on 27 July.
The committee was told that, according to the latest Eurobarometer poll, 80 per cent of Europeans want the EU to do more to tackle security threats.