King, speaking at a parliamentary committee, said the threat posed by Isis and other terrorist organisations was even more dangerous because they "know no national borders."
"That is why," he told MEPs, "we need a European response to this threat."
Security union Commissioner King was appearing at an inter-parliamentary committee meeting with national parliaments on Monday.
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The hearing was organised by the civil liberties, justice and home affairs committee with the support of national parliaments.
The official said the role of Europol was "crucial" in the fight against the continued threat from terrorists and organised crime.
"It plays a critical role and has unique crime-fighting capabilities," said King.
However, he went on to concede that in the public's eyes the agency, based at The Hague and headed by fellow Briton Rob Wainwright, still "needs to be seen as being legitimate."
The meeting was a chance for MEPs and representatives of national parliaments to discuss the framework of EU internal security policies and the democratic oversight and scrutiny of Europol's activities.
Labour MEPs warned that this will be something UK MEPs will no longer be involved in after Brexit.
UK MPs and peers, including Yvette Cooper - Chair of the UK home affairs select committee - were among those who questioned King and Wainwright on the development of an EU security union and best practices for parliamentary scrutiny at the national level.
The meeting follows the UK government's recent confirmation it will remain part of Europol and continue to opt into cross-border crime fighting measures.
UK Socialist MEP Claude Moraes, Chair of the civil liberties, justice and home affairs committee, said, "The decision that Britain will remain part of Europol is important for our security and safety, and recognises that the agency has a crucial role to play in effectively targeting cross-border crime and combatting terrorism.
"It is, however, equally important that European and national parliamentarians continue to have a role in scrutinising the agency to ensure that the delicate balance between security and civil liberties is maintained - yet for the UK, our ability to scrutinise key measures and influence policy will be at risk after Brexit."
Moraes added, "The discussion was also an opportunity to debate how to make the security union a reality with key British officials working in this field and once more, as a consequence of Brexit, we will lose this influence."
He said, "The meeting was an opportunity for European and national parliamentarians to emphasise the need for existing legislation to be implemented and acted upon by national governments.
"We will only be able to derive the benefits of greater cooperation in the field of security if anti-terror and anti-radicalisation measures are fully implemented by all EU countries.
"We met with national parliaments in order to discuss EU internal security policies and develop the format for the democratic scrutiny of Europol, which represents a major plank of Britain's security arrangements with the EU.
"The new regulation will strengthen Europol to ensure it is fully equipped to fight terrorism, cybercrime and the rise in cross-border crime, and that MEPs and representatives from national parliaments will scrutinise the agency in order to ensure that fundamental rights are upheld," added Moraes.