Barnier and his British counterpart, Brexit Secretary David Davis, told reporters on Thursday there had been some progress this week on the other two issues around Britain's March 2019 withdrawal from the bloc on which the European Union demands "sufficient progress" before it will agree to discuss a transition and future relationship.
"(We) also want to ensure that we get onto that business of talking about the future relationship, the future partnership we're going to have with the EU.
The gridlock means that the EU's 27 remaining leaders will decide against starting discussions on a post-Brexit trade deal with the United Kingdom when they meet in Brussels next week, or on a transitional arrangement to cushion the impact of separation.
But he added: 'This week, however, the United Kingdom repeated that it was still not ready to spell out these commitments.
Mr Barnier's comments, which appear to be as much aimed at EU27 leaders as Britain, came after his counterpart made his most open plea yet for the bloc to alter its negotiating stance.
While that is unlikely to happen, Barnier has been pushing member states for making a gesture towards the United Kingdom by pledging to "scope" the positions on transition within the EU-27.
Barnier has not not reveal if he would press European Union countries to begin "scoping" the transition.
"There is a new momentum and I remain convinced today, with the political will, decisive progress is within our grasp within the next two months", he said.
Barnier described the stalemate as "very disturbing" and added that he was advising leaders that not enough progress had been made to move on to trade negotiations.
"But today I can confirm that we want to reassure those European citizens living in the United Kingdom that their rights and status will be enshrined in UK law by the Withdrawal Agreement", Davis added.
"I hope the member states will see the progress we have made and take a step forward" next week, British Brexit envoy David Davis told reporters.
"I make no secret of the fact that to provide certainty we must talk about the future", Mr Davis said.
The issue of citizens' rights is one of the main issues to be dealt with during the negotiations, together with the land borders between Northern Ireland and the Republic of Ireland as well as Gibraltar and Spain, plus immigration control and access to the European single market.
On the latter issue differences still remain over the European Court of Justice's role in guaranteeing those rights, family unifications and the exporting of United Kingdom benefits.