He said progress was needed to "address the direct and often disproportionate impact that aspects of the protocol are having on the citizens of Northern Ireland, contrary to its intended purpose", according to a United Kingdom government spokesperson.
Commission vice-president Maroš Šefčovič said in a statement that UK's decision to unilaterally extend a grace period on checks for goods moving between Britain and Northern Ireland amounts to "a violation" of the so-called Northern Ireland Protocol.
The paramilitaries including the Ulster Volunteer Force, Ulster Defence Association and Red Hand Commando said they were concerned about the disruption to trade between Great Britain and Northern Ireland due to the Brexit deal.
The LCC represents three militant groups that were responsible for many deaths during 30 years of conflict between pro-UK unionists and pro-Irish republicans, before the peace was sealed in 1998.
Since it left the European Union past year, Britain's relations with the bloc have soured, with both sides accusing the other of acting in bad faith in relation to part of their trade agreement that covers goods movements to Northern Ireland.
It has caused disruption to some goods travelling from the rest of the United Kingdom after suppliers encountered extra red tape.
Speaking on RTÉ Radio 1 this week, Minister Coveney accused the British government of breaking the Northern Ireland Protocol, as well as its own promises.
"We continue to work closely with them through the Joint Committee process and remain committed to the Northern Ireland protocol but we want to address those areas where there are issues that have arisen".
"As part of the pragmatic and proportionate implementation of the Northern Ireland Protocol, the government is taking several temporary operational steps to avoid disruptive cliff edges as engagement with the European Union continues through the Joint Committee", Northern Ireland Secretary Brandon Lewis said.
The British government extended a grace period for some checks on agricultural and food products imported by retailers to Northern Ireland until October 1 in a move it said was necessary to ensure the free flow of goods to the British region.
Prime Minister Boris Johnson was asked about the protocol issues during a visit to Teesport in Middlesbrough on Thursday
"Grace periods do not provide the long-term certainty that businesses and consumers in Northern Ireland require".
1 April/1 October: End of a grace period for supermarkets, which will now need health certificates to move agri-food goods from Great Britain to Northern Ireland.
But its announcement offers more evidence that Northern Ireland's delicate balance of peace is being destabilised as a result of Brexit, with unionists furious over new border checks that they say are separating them by stealth from the rest of the UK.
He said: 'I made clear to them my regret that the UK had moved in a unilateral way, rather than working in continued partnership with the EU in accordance with the EU-UK joint statements of 11 and 24 February'.
The party's Westminster leader, Sir Jeffrey Donaldson, said: 'Whilst supermarkets and those bringing in goods via our ports from Great Britain will be relieved to see extensions to the grace periods, we will be continuing to press the Government for a permanent solution.
Shortly afterwards, his Northern Ireland minister, Brandon Lewis, announced the extension of the grace period.
But this means there has to be customs declarations on goods entering Northern Ireland from Great Britain, including checks on some products.
Coveney's words came after the move by the British government to unilaterally change how the Northern Ireland Protocol is implemented.
'The protocol has been demonstrated to be unworkable'.