EU Commissioner Phil Hogan has described the mood music as good and said he remained cautiously optimistic about making progress on a Brexit deal in the coming days.
He said the Taoiseach knows what is at stake and risks have to be taken in relation to achieving the right outcome.
Mr Hogan said talks between the UK and EU had stalled recently and that yesterday's meeting would create renewed momentum in negotiations in Europe over the coming days.
He said nobody wanted to see a no-deal Brexit and that the protection of the Irish economy and the Good Friday Agreement was paramount.
Mr Hogan said the use of words like 'pathway' in relation to yesterday's talks indicated progress was being made.
He said the issues of customs and consent were of serious concern to the EU and the UK and the aim was to ensure no hard border on the island of Ireland, and to have as frictionless trade as possible between Europe and the UK.
Commissioner Hogan said he hoped the talks between Leo and Varadkar and Boris Johnson would unlock the impasse and create new impetus in the coming days of negotiations.
He said the EU was still hopeful of a deal and working towards that end but he said Europe had to meet the objectives set out in the mandate of the EU 27.
He said one of those key issues was the protection of the Good Friday Agreement and protecting the peace of the island of Ireland.
The commissioner said Boris Johnson is now trying to fine tune the deal negotiated by Theresa May to get it through parliament and he said he believed the House of Commons would approve such a deal.
In the event of a no-deal Brexit he said all the necessary financial support and policy measures were in place to deal with such a scenario.
But he added a no deal crash out would mean that the issues currently on the table would still remain and have to be renegotiated.