By Kylie MacLellan

LONDON (Reuters) - Scotland's First Minister Nicola Sturgeon on Sunday softened her stance on the potential timing of a second independence referendum after Prime Minister Theresa May rejected her call to hold a vote before Britain leaves the European Union.

Sturgeon had called for a referendum to be held between autumn 2018 and spring 2019 but after May said "now is not the time", the Scottish leader said she could be prepared to hold a vote later as long as it was not too long after Brexit.

"It is for (May) then to say what timescale she thinks would be appropriate and then yes I am happy to have that discussion within reason," Sturgeon said during an interview with ITV.

Asked if a vote in 2021 would be reasonable, Sturgeon said it would not because too much time would have lapsed after Britain's EU exit, due in late March 2019, and there could have been too much divergence in areas such as regulations.

"Then gets much harder for Scotland to seek a different course. But if she is talking in the spring of 2019, a bit later perhaps than I was suggesting then there may be some room for discussion around that," she said.

Sturgeon's comments came as a Panelbase poll for the Sunday Times, carried out since her announcement that she would seek a fresh referendum, put support for independence at 44 percent, while 56 percent backed staying in the United Kingdom.

It also found 51 percent of Scots did not want a vote on independence within the next few years.

Ruth Davidson, the leader of May's Conservative Party in Scotland, said any vote could not take place until "after the Brexit process has played out" so that the Scottish people know what choice they face.

"I don’t think you can have an independence referendum again if you don’t have public consent for it and the people of Scotland don’t want this," she told the BBC TV.

"The SNP is not Scotland and they are acting against the majority wishes of the people of Scotland."

Scots rejected independence by 55-45 percent in a referendum in September 2014. But majority of Scots voted in favor of Britain staying in the EU in June.

In a separate interview with Sky News, Sturgeon said her party was currently looking into the currency options for an independent Scotland but "the starting point of our consideration" would be that it continues to use sterling.

Earlier this week her predecessor, Alex Salmond, told the Financial Times that Scotland could abandon a currency union with the rest of the United Kingdom.

"We will set out a very clear proposition but I think it is right ... that we do very serious work before we come to putting that proposition forward," Sturgeon said.

(Reporting by Kylie MacLellan; Editing by Clelia Oziel)