Sterling held at $1.2911 after Britain's parliament backed a withdrawal deal, but rejected the government's tight timetable, while European Union members delayed deciding whether to grant a three-month extension to the October 31 leaving date.
The pound has soared 6% in two weeks of volatile trade since British Prime Minister Boris Johnson flagged and then clinched a deal with the EU on the terms of Britain's exit from the bloc.
"Sterling remains at the centre of the focus for forex markets," said Michael McCarthy, chief market strategist at brokerage CMC Markets in Sydney.
"It looks like traders are weighing up the current parliamentary shenanigans versus the seeming inevitability of a Brexit," he said.
For now, the dollar was steady in Asian trade, gaining marginally against the Australian and New Zealand dollars while slipping marginally against the euro and Japanese yen.
Against a basket of currencies the dollar was flat at 97.459.
It stood at 108.65 yen, and drifted higher from a five-week low touched against the kiwi on Tuesday, with the New Zealand dollar buying $0.6420. The Australian dollar bought $0.6851.
The Chinese yuan was flat at 7.0623 in offshore trade.
The euro held at $1.1132 with traders looking to euro zone manufacturing and services data and the outcome of a European Central Bank meeting, both due later on Thursday.
Crypto-currency bitcoin plunged as far as 11% overnight to a 5-month low of $7,258.00 after Facebook CEO Mark Zuckerberg sounded downbeat about the prospect of Facebook's crypto project, Libra.
Also weighing on the digital currency was the announcement from Google that it has achieved a breakthrough in research on a quantum computer.
If fully developed, a vast computing power of quantum computer is expected to obliterate existing cryptographic technologies.
Commonwealth Bank of Australia analysts reckon the pound will stay rangebound between $1.3000 and $1.2800 until things become clearer.
European Council President Donald Tusk said he recommended the leaders of the EU's 27 other member states back a delay, with senior EU diplomats saying a three-month delay is most likely.
Other majors were stable without much news to move the greenback.
"With trade negotiations now moving out of the headlines, there doesn't seem much to spur the dollar in either direction," CMC Market's McCarthy said.
Positive comments from US and Chinese leaders earlier in the week about progress negotiating a truce in a their trade dispute had rallied trade-exposed currencies. That has begun to run out of steam as concerns about the health of the US economy returned to the fore.
Tech industry bellwether Texas Instruments posted a disappointing earnings outlook on Tuesday, followed overnight by signs of a slowdown in Microsoft Corp's cloud computing division.