He described himself as "stubbornly optimistic" that a deal is within reach.
European Union diplomats said his aim was to talk up the trade deal in order to entice Britain into accepting it and an Irish border emergency plan - a key sticking point in Brexit talks.
The Pound-to-Dollar exchange rate is trading 0.91% higher at 1.2982.
His comments set the stage for the contentious Irish issue to remain at the centre of talks over the next six weeks, ahead of a summit of European Union leaders in October that London continues to see as the deadline for a deal to be reached.
The pound is now in retreat from its overnight rally.
Mr Raab told reporters: "On Northern Ireland we remain committed to giving effect to the Joint Report [of last December], continuing the work on the potential solutions, working with Michel and his team on some of the issues he's raised. It's essential to conclude negotiations, because - as I've said - with no backstop, there can be no agreement".
While this doesn't mean the EU's red lines have changed - in fact he explicitly confirmed that they must be respected, along with the UK's - it does suggest that more constructive conversations can happen to find a workable solution that suits both sides, should one exist.
The French politician also delivered a blow to the key element of the prime minister's Chequers plan for the future relationship, which would see the United Kingdom remain in the single market for goods only. But it cannot be built to the detriment of who we are.
This week, implied market volatility on the British currency has also risen more than its counterparts in the euro and the Japanese yen.
Barnier, who is tipped to become European Commission president, dismissed a suggestion that Brexit talks had become a poker game, saying negotiations were "far too serious" to be talked about in such terms and would produce "no winners".
After meeting British Brexit minister Dominic Raab in Brussels, Barnier hailed progress on some security issues but warned there were still major differences over protected geographical indicators like champagne and stilton - and Ireland.
If markets remain optimistic about the chances of a strong UK-EU Brexit deal, the pound to USA dollar exchange rate could continue its recovery in the coming days.