On a visit to the border region, European Union negotiator Michel Barnier said "we need to agree rapidly by June on the scope of all-island customs and regulations, the safety and controls that we need to respect the single market".
Taoiseach Leo Varadkar has said Brexit concerns are partly responsible for the powersharing impasse at Stormont.
She rules out the idea of Northern Ireland remaining in a customs union, aligned with single-market regulations, as this would have the effect of creating a customs border within the UK.
However the taoiseach's press office said: "As is standard protocol, the Northern Ireland Office was informed".
However, it is understood that such protocols have been relaxed in north-south relations over time, but that the government still considers that it is up to Dublin to inform Northern Ireland elected representatives if an Irish minister is visiting their constituency.
This summer's meeting of European leaders in Brussels would be a "stepping stone" for the final summit in October, which is the deadline for reaching an agreement on withdrawal, he added.
"I am not willing to engage in any kind of polemics with Mrs Foster", he said.
TUV leader Jim Allister said the visit shows that "the pattern of seeking to lord it over us is clear".
He added: "The backstop is not there to change the UK's red lines". These days, in contrast, one can drive across the border without noticing it. Security measures were phased out following the Good Friday peace agreement of 1998, and the EU's single market and customs union have banished the need for inspections of imports and exports between the two countries.If the United Kingdom leaves the single market and customs union, as Theresa May's government intends, those inspections will return in some form.
He inadvertently had a dig at Davis when he took a question from a Northern Irish journalist about Davis believing the backstop wasn't necessary.
The Irish Government's position is resigned to focusing on getting the British government to come up with a satisfactory interpretation of the backstop - or Option C. "His proposal of us being in an all-Ireland regulatory scenario with a border down the Irish Sea simply does not work".