Michel Barnier has urged rapid agreement by June on the Irish border.
The scope of all-island customs and regulations needs to be settled between Britain and the EU, the bloc's chief negotiator added.
Many of the operational details have yet to be agreed and the vexed question of the UK's only land border with an EU state after Brexit is at the centre of intensive work by officials at present.
Mr 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."
He said the June 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.
A joint report on the UK's withdrawal agreed in December by Prime Minister Theresa May and European Commission president Jean-Claude Juncker included both British proposals, along with a third "backstop" option which would keep Northern Ireland in the customs union.
But a version published by the EU in February and agreed by the EU27 last month contained only the "backstop", effectively drawing a customs border down the Irish Sea, which a furious Mrs May said "no British prime minister could ever agree".
Mr Barnier visited the Irish border town of Dundalk, Co Louth, for a conference on Monday.
He said: "We want to succeed with the UK, not against the UK.
"Together with the Irish government we are looking for practical solutions."
On Monday he delivered a keynote speech during a meeting of the Irish government-hosted All-Island Civic Dialogue on Brexit in Dundalk.
He then crosses the frontier to Newry in Co Down for meetings with business leaders.
On Tuesday Mr Barnier will visit the other, north-western end of the porous 310-mile border at Londonderry.
It is his third visit to Ireland and Irish foreign affairs minister Simon Coveney said he was a friend of the country.
Earlier, DUP leader Arlene Foster said Mr Barnier did not understand unionist culture.
She told the BBC: "He's hearing a very strong message from the Republic of Ireland's government, he's hearing it from Sinn Fein.
"We have tried to get him to understand the unionist position for the people of Northern Ireland, but he hasn't really responded to that and I'm disappointed about that.
"I am also disappointed that he will hear anti-Brexit voices tomorrow, he won't hear any pro-Brexit voices tomorrow because he is being taken around by Sinn Fein MPs."
In response, Mr Barnier said: "My door is open."