The taoiseach has held Brexit talks with European Council president Donald Tusk in Dublin.
Leo Varadkar welcomed Mr Tusk on Tuesday morning in front of the media, but neither of the men made any reply when questioned by journalists.
When asked if Monday's Westminster news posed a problem, Mr Tusk did not reply but shrugged.
The Dublin meeting was to consider any requests from the UK to delay Brexit, and other issues on the EU agenda, ahead of the European Council meeting in Brussels later this week.
A joint statement after the meeting said they discussed the current state of play regarding Brexit.
"President Tusk expressed the strong and ongoing solidarity with Ireland of the European Council and European leaders," the statement read.
"They agreed that we must now see what proposals emerge from London in advance of the European Council meeting in Brussels on Thursday.
"Meanwhile, preparations continue in Ireland and across the European Union for a no-deal scenario, which would have serious consequences for all concerned."
Speaker of the House of Commons John Bercow provoked uproar at Westminster on Monday when he ruled that the British government could not bring the prime minister's deal back for a third "meaningful vote" unless there were substantial changes.
The Speaker's ruling was welcomed by some Tory Brexiteers opposed to Theresa May's deal, who argued that it increased the chances of a no-deal break.
Brexit Secretary Stephen Barclay has indicated ministers will continue to press on with Mrs May's Brexit deal despite Mr Bercow's ruling.
