By David Hughes and Michael McHugh
There is no reason why the European Union cannot have a "strong relationship" with the UK after it leaves the bloc, Michel Barnier said.
He expressed regret at Brexit, warning it would "come at a cost" to both Britain and the remaining 27 members of the EU and would bring consequences, but his objective was to reach a "fair deal".
Protecting Irish interests as part of the Union would be an important part of the Brexit negotiations, with efforts to avoid a hard border and protect the peace process central to the talks, Europe's chief negotiator told Ireland's parliament.
He added: "If the conditions are right, a close partnership with the UK is in everybody's interest. And in Ireland's interest in particular."
He said he hoped to negotiate a "bold and ambitious but fair free trade agreement" but only once progress has been made on issues including the UK's bill for leaving the EU.
Mr Barnier was being given a privilege normally only afforded to visiting heads of state and prime ministers, and he joins luminaries such as Nelson Mandela and Bill Clinton in addressing both houses of parliament.
In an apparent reference to the diplomatic row caused by the leaks following European Commission president Jean-Claude Juncker's meeting with Prime Minister Theresa May, Mr Barnier called for "mutual respect" in the talks.
Mrs May has accused Brussels insiders of seeking to influence the outcome of the June 8 General Election.
Mr Barnier said: "If we put things in the right order, if we negotiate with mutual respect, without any kind of aggressivity... if we are open to finding solutions, there is no reason why a strong Europe cannot maintain a strong relationship with the UK."
Acknowledging the particular issues Brexit poses to Ireland, Mr Barnier said: "I want to reassure the Irish people: in this negotiation Ireland's interest will be the Union's interest.
"We are in this negotiation together and a united EU will be here for you."
He restated the EU's insistence that the issue of the UK-Ireland border, citizens' rights and "the financial settlement" must be the first priorities for talks.
"We first must make sufficient progress on these points before we start discussing the future of our relationship with the UK.
"The sooner this will happen, the better."
Mr Barnier said he wanted the relationship between the UK and EU to extend beyond trade, with co-operation on other cross-border issues.
He said: "We want these negotiations to succeed. I want us to reach a deal.
"The UK has been a member of the EU for 44 years. It should remain a close partner.
"We will need to negotiate a 'bold and ambitious' but fair free trade agreement.
"But we will need the same ambition for our research and innovation networks and for the fight against climate change.
"We need the same ambition in international co-operation and development."