Mayor of London Sadiq Khan visited Dublin on Thursday and argued against the prospect of a "devastating" no-deal Brexit.
President Michael D Higgins welcomed Mr Khan to his home in Aras An Uachtarain on Thursday morning.
Mr Khan congratulated Mr Higgins on his recent re-election before the two discussed a wide range of issues of mutual concern, including climate change, sustainable development, housing, transport and 'Brexit'.
A statement from the President said Mr Higgins also expressed; "sympathies and support for the people of London, who have experienced a number of terrorist attacks in recent years, and the tragedy of Grenfell Towers".
After the visit Mr Khan took to social media, saying: "London just wouldn't be the city it is without the contribution of the Irish community.
"Today I made sure President Higgins knows London is and always will be open to our Irish friends."
Mr Khan went on to visit the Dublin Chamber of Commerce and met with students of Trinity College where the topic of Brexit was continually raised.
"The worst possible outcome, which remains a grave concern given the political uncertainty in Westminster, is that the UK leaves the EU with no Brexit deal at all," Mr Khan said in a speech.
"This would not only be devastating for London's economy, but would actually hurt businesses and economies across Europe, including here in Dublin, and increase the chance of a hard border on the island of Ireland.
"In my view, the prospect, the very notion, of a no-deal Brexit must be taken off the table by the British Government.
"It's just too dangerous to leave as a possibility.
"That's why, today, I'm calling on Theresa May to withdraw Article 50 if the British Parliament rejects her deal next week, which is looking extremely likely.
"This move would be the single best way to guarantee that we avoid falling off the cliff edge.
"It would stop the clock that is ticking down towards a no-deal Brexit, and it would provide the breathing space to decide how we resolve this mess.
"If the British Prime Minister refuses to take this precautionary step, we would continue heading towards a no-deal Brexit in just a few months.
Mr Khan also held talks with the Taoiseach Leo Varadkar and met Minister of State for European Affairs Helen McEntee in Dublin's Government Buildings.
Speaking on social media the Taoiseach said he was "looking forward to return visit" to London after meeting with Mr Khan.