Mr Barnier warned that agreement on transition was far from "a given", and was conditional on agreement on the withdrawal agreement.
The EU negotiator's stark message, which weakened sterling, came after EU diplomats and officials warned in recent days that sticking points in the talks were threatening the whole Brexit schedule that the two sides had agreed on to provide certainty to business and citizens.
"The time has come to make choices", Barnier repeated his message from Monday when he met with May in London.
But the British currency quickly reversed those gains on Friday after the EU's Michel Barnier said London had "substantial" objections to the EU's transition offer and that parts of it were not up for negotiation.
The EU has a large number of worldwide agreements which underpin relations with more than 100 so-called third countries, covering issues such as trade, nuclear cooperation and aviation.
Barnier's remarks triggered an immediate drop in the British pound's value on Friday as 1 pound was traded at 1.37 USA dollar after a 1.1 pecent loss.
Barnier said Britain has to accept the "consequences" of its decisions.
"The UK insisted that we should reach an agreement in March on transitional period".
Britain wants a transition after Brexit that will avoid businesses having to adjust to new rules and regulations twice.
GETTYThe backbench Tory MP is head of the influential European Research Group
The British nationals' lawyer, Christiaan Alberdingk Thijm, said: "This is a great victory because the questions are very important questions about the interpretation of law around European Union citizenship".
Mr Barnier sealed the state of mutual incomprehension, telling reporters in Brussels that he had "problems understanding the UK's position" on the transition period. He admitted there were "still things incomplete" but said that "a great deal of progress has been made".
"The UK wants to enjoy the advantages of the single market, the customs union and common policies".
The U.K., the European Union and Ireland all have indicated that they would like to keep the seamless Irish border in a solution that is in line with the 1998 Belfast (Good Friday) Agreement that brought peace to the region after years of violence.
Barnier also voiced surprise at the U.K.'s objection to a fast-track process that Brussels has proposed for adjudicating any disputes over European Union rules that might arise during the transition - with the disputes essentially settled immediately in the EU's favor.
He said his approach "not been in the least discourteous or vindictive".
The strategy document is alleged to have concluded that the movement "must then win the meaningful vote" that Prime Minister Theresa May has pledged on the final Brexit deal and if she loses that vote, "it is likely to trigger a new referendum, or election".