Mr Michel said Brexit is not just an Irish issue, but also a European one, and added that the coming days will be “crucial” and a “moment of truth”.
Speaking at Government buildings in Dublin, Mr Michel said: “My message is simple: the EU stands in full solidarity with Ireland.
“This is especially true when it comes to the full implementation of the Withdrawal Agreement and the protocol on Ireland and Northern Ireland.
“This text has been negotiated for three years, each word, each comma has been debated for hours and hours. It has been modified by both parties. There is simply no question of its full implementation.”
Mr Michel said he had been “very clear” with British prime minister Boris Johnson: “It’s now for the UK to restore trust and to put all its cards on the table.
“The EU is doing its utmost to find an agreement with the UK, but not at any cost.”
Mr Michel said “significant steps” needed to be taken by the EU’s “British friends” in the coming days if agreement was to be reached.
“The coming days are crucial, this is the moment of truth,” he said.
“There is only one week to go before the European Council on the 15th and 16th of October.”
Also speaking after the meeting, Taoiseach Micheál Martin described the Brexit negotiations as “very challenging”.
Mr Martin said: “There needs to be movement in terms of getting into end-stage negotiations and we feel there’s a lot of work to be done yet on a number of fronts, and it’s quite a challenging task ahead of the negotiators to ensure that an agreement is arrived at.”