Speaking ahead of a Brexit summit in Brussels, Malmstrom said the Europeans "see this merely as preparations being made by the U.S.to negotiate with them and others".
Mr Coveney told BBC Radio 4's Today programme: "What Michel Barnier is now suggesting is, look, let's ensure that the backstop is never likely to be used by creating the space and time for the United Kingdom and the European Union to be able to negotiate UK-wide customs arrangements that can ensure that there won't ever be the need for customs checks between Britain and Northern Ireland".
The UK is due to leave the EU next March and it had been hoped that on Wednesday, EU leaders would agree that enough progress had been made to call a special Brexit summit in November to finalise and formalise the divorce deal.
At present the two sides are proposing that Britain remain inside the European Union single market and bound by its rules from the time it leaves the bloc in March until December 2020, to give time for new trade relations to be set up.
But, after Britain's refusal to accept an indefinite legal "backstop" to prevent the return of a hard border between Northern Ireland and the Irish Republic, doubts are mounting.
If the existing transition expired before it was ready, then the original Northern Ireland-specific backstop would have to kick in.
But her own Eurosceptic Conservative MPs are demanding this "backstop" arrangement be time-limited, something the European Union will not accept.
But after hastily arranged talks between the EU's chief negotiator Michel Barnier and Brexit Secretary Dominic Raab broke up on Sunday without agreement, the negotiations are once again deadlocked.
Britain says it has not asked for an extension, but May has not yet come up with proposals for unblocking the border logjam.
Her idea is that a future trade arrangement would be so comprehensive as to avoid the need for border checks on the island of Ireland.
Despite her appearance, any hopes of a Brexit deal breakthrough is as low as it has ever been in recent weeks.
On Monday, DUP deputy leader Nigel Dodds threatened to frustrate Theresa May's minority government should any Brexit deal "break up or fracture" the Union.
Citing a German government document, the Frankfurter Allgemeine Zeitung newspaper reported late on Tuesday that the European Commission had offered to allow Britain - "in a good will gesture" - to remain in the EU customs union and internal market beyond an agreed transitional arrangement until the end of December 2020.
"I'm convinced that if we as a government stand together and stand firm, we can achieve this", she said, according to her spokesman.
"I think we are quite close to a no-deal", warned Konrad Szymanski, the Polish minister for European Affairs, after a pre-summit meeting with his European counterparts in Luxembourg.
The U.S. administration has notified Congress that it will seek trade pacts with the EU, Japan and Britain.
He said his party would stop short of pulling the government down and triggering a general election, but added: "Under the fixed term parliament act there is a lot we cannot support in terms of the government's domestic, financial, welfare and other legislation which does not trigger Jeremy Corbyn getting into Number 10".
British opponents of Brexit say the United Kingdom won't be able to strike a trade deal with the USA unless it weakens its current EU-level protections on workers rights, animal welfare and environmental protection.