Latvian MEP Artis Pabriks, Parliament's rapporteur on the European border and coastguard regulation, said the migrant crisis had been a "wake up call" for Europe, and that it had highlighted its "inability" to fully assess the situation on the EU's borders.
The former government minister said the Parliament's justice committee is expected to vote on a report he has drafted on the issue on Monday.
Meanwhile, improving the management of the EU's external border is no longer just an aim; it is an emergency, according to an EESC opinion adopted on Thursday.
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But this should not be done at the detriment of fundamental human rights, notably the right to asylum and the right to free movement in the EU, says the document which is not legally binding.
The EESC, while calling for a strengthened mandate for the Frontex agency, says it does not support the European Commission's proposal to establish systematic checks on EU citizens at the external borders of the EU, as this would dramatically affect the fundamental right to free movement.
Instead, the EESC proposes to reinforce and consolidate the Schengen rules by applying them uniformly across all member states.
This new form of border management must go hand in hand with a transformation of the Frontex agency into a European Border Guard, as proposed by the European Commission.
Italian member Giuseppe Iuliano, EESC rapporteur on the issue, said, "The European Border Guard should be empowered to effectively manage the EU border and support member states dealing with overwhelming migration pressure.
"In return, the agency should be governed in a transparent manner and there should be more accountability to the EU member states and citizens."