LONDON- The pound fell towards $1.32 on Monday as Prime Minister Theresa May sought to salvage her Brexit deal by winning over doubtful lawmakers with threats and promises to avoid any move to oust her.

May is expected to table a third vote on her Brexit deal on Tuesday or Wednesday, after it was heavily defeated twice in large-scale rebellions by Eurosceptic Conservative lawmakers and by members of Northern Ireland's Democratic Unionist party.

She suffered a further setback on Monday when Boris Johnson, the Brexiter former foreign secretary, refused to back her agreement unless she secured changes to the Irish backstop — designed to prevent a hard border on the island of Ireland.

Another Brexit-supporting British lawmaker said a "lot of people" in parliament still remained opposed to May's European Union withdrawal deal. 

Analysts, however, said the pound could enjoy gains this week.

"Should May hold another vote tomorrow that would constitute a signal that she considers it possible that her deal will be accepted," said Ulrich Leuchtmann, a currency strategist at Commerzbank.

"It should no doubt have a moderately positive effect on the British currency," he added.

Sterling traders are bracing for further volatility as May scrambles to convince lawmakers to back her deal ahead of the parliamentary vote so that she can attend a European Summit on Thursday and offer leaders something in return for more time.

The pound was down 0.4 percent at $1.3245 . It was also weaker against the euro, down half a percent at 85.62 pence. Last week the currency swung wildly, trading between extremes of $1.2945 and $1.3380.

It has struggled to hold onto last week's gains as traders contemplate the array of possibilities that have opened up including a second referendum or general election.

Options markets show implied sterling volatility -- a gauge of expected swings in a currency -- still elevated, with one-week vols near multi-month highs. Sterling vol is higher than G10 as well as many emerging currency peers.

"With sterling one-week implied volatility suggesting the currency is coiled like a spring, there is a path for a substantial upside break-out - were a benign path of Brexit events to unfold," said Chris Turner, head of foreign exchange strategy at ING in London.

(Reporting by Tom Finn Editing by Peter Graff) ((tom.finn@tr.com; +44 2075427508 ; Reuters Messaging: tom.finn.reuters.com@reuters.net))