British Prime Minister Theresa May failed to clinch such an agreement during a lunch in Brussels on Monday, after a tentative deal with Dublin to keep EU rules in Northern Ireland angered her allies in Belfast.
During a volatile day of trading on Monday, the pound had climbed on prospects of free trade and perhaps a very "soft Brexit". But a sell-off was triggered when Northern Ireland's Democratic Unionist Party (DUP) issued an uncompromising reiteration of its refusal to accept any "divergence" from rules on the British mainland.
Sterling, which had hit two-month highs of $1.3550 at the end of last week, slipped to as low as $1.3370 in early trade in London on Tuesday, before edging up to trade around $1.3420 by 1020 GMT. That still left it almost half a percent down on the day.
"Some concern is emerging over whether an agreement will be reached this week, and is generating fresh sterling selling," said Mizuho's head of hedge fund currency sales, Neil Jones.
Britain's finance minister Philip Hammond said on Tuesday he was "very confident" a deal between the EU and Britain could be reached this week.
May and other British officials will speak to the DUP later in the day, an official said, and could return to Brussels as early as Wednesday to try to save a deal.
BNP Paribas currency strategist said the market was still pricing in a positive outcome from the EU summit on Dec. 14-15, and that sterling looked vulnerable.
"What we're likely to see on an announcement (of a deal) is sell-the-fact price action," he said. "The market is already positioned with a small net long position and the likelihood of them wanting to build that position out further is small."
Other analysts argued sterling's losses were likely to be limited.
"The immediate fallout should be limited as markets have become well-versed with the idea that Brexit won't be solved overnight," ING said in a note to clients. "We remain constructive on sterling."
Data showing Britain's dominant services sector lost speed in November as prices charged by companies rose at their fastest pace in nearly 10 years - potentially adding to the country's inflation problem - had only a small further negative effect on the pound.
Against the euro, it traded down 0.3 percent at 88.34 pence .