A Downing Street spokesperson said: "Both sides strongly reiterated their desire to reach a Brexit deal".
The Prime Minister's chances of a breakthrough with Brussels were looking increasingly unlikely on Tuesday after accusations from Number 10 that the bloc was making it "essentially impossible" for Britain to leave with a deal.
The President of the European Parliament David Sassoli has said there has been "no progress" on a Brexit deal following a meeting with Prime Minister Boris Johnson.
He said it was unacceptable for Northern Ireland to stay in the customs union and that Johnson had told Merkel that the United Kingdom had made a significant offer and that it was time for the EU compromise.
That's something the British government says it can't accept.
After the pair met in 10 Downing Street, the newly elected president said he hoped to hear proposals to take negotiations further.
How people and goods will move across the Irish border is the main sticking point in a deal.
The no-deal Brexit is upon us now. Lord Lilley went on to claim the new deal being offered would require a lot of work but did still have major concessions from the UK.
"Boris Johnson, what's at stake is not winning some stupid blame game", he wrote on Twitter. "At stake is the future of Europe and the United Kingdom". But, under English law, he also is required to seek an extension if he doesn't have a deal by October 19 - something that may still force him to seek a delay and hold a general election before going back to Brussels again.
Britain is due to leave the European Union on October 31, more than three years after the country narrowly voted in a referendum to end its nearly five-decade membership of the bloc.
With an extension of the UK's European Union membership now looking inevitable, other diplomatic sources suggested an unlikely outlier for an end date could even be ahead of a possible general election so as to force the Commons into accepting a deal.
Despite this, he said he felt uncertain over Mr Johnson's Brexit alternative to the Irish backstop.
The UK government has put forward nothing credible to deal with border issues in Ireland.
The Institute for Fiscal Studies think-tank meanwhile warned that "even a relatively benign no-deal Brexit" would see Britain's debt burden surge to 50-year highs.
Scottish First Minister Nicola Sturgeon, who opposes Brexit, tweeted: "The UK government's attempts to shift the blame for the Brexit fiasco to anyone but themselves - today it's Merkel - is pathetically transparent".
As the clock ticks down, a new Brexit readiness document is expected to be published on Tuesday subject to the Speaker approving a statement by no-deal planning chief Michael Gove. The government says those plans will minimize any resulting economic shock.
He said he would abide by the law but Britain would leave the European Union by the end of the month without explaining that contradictions.
In his interview with RTE, Mr Varadkar was asked whether he was concerned the language around the talks was "getting toxic".
The source quoted by the Spectator appeared to have two views about a delay: that the government could frustrate a delay but that if it was forced to extend Brexit then it would fight an election calling for an immediate no-deal exit.
Mr Mr Johnson, who took over from Theresa May in July, has been accused of political manoeuvring before calling a snap general election to strengthen his position in parliament. This week's shorter suspension is more routine.
India announces fifth interest rate cut, loans to be cheaper
While rate cut is nearly certain, the quantum of cut and the policy stance will be keenly watched by the market participants. The central bank said the decisions are in consonance with its medium-term target of 4 per cent for consumer inflation.