Nicola Sturgeon has said she is willing to have a “reasonable” discussion with Theresa May to delay a Scottish independence referendum, but insisted it could not be put off for long in the face of Brexit.

Scotland’s first minister earlier said a new independence vote should be held in 2018, before the final deal on the UK’s exit from the EU is sealed. But on Sunday she hinted that she could be willing to wait up to another year.

May has said she will not agree to any referendum taking place before Brexit, telling Sturgeon “now is not the time” for the vote to be re-run.

Sturgeon said she was still offering compromise. “[May] said she does not agree with that timescale,” the first minister told Peston on Sunday. “I think it is for her then to say what timescale she thinks would be appropriate and I’m happy to have that discussion within reason.

“If she’s talking in the spring of 2019, a bit later perhaps than I was suggesting, there may be some room for discussion around that. But it seems to me to be just fundamentally unfair for a UK government, with Brexit having sunk the ship, trying to puncture Scotland’s lifeboat as well.”

Sturgeon added that a delay until after the next Scottish parliamentary elections in 2021 would not be acceptable. “I don’t think that is reasonable because by that point Scotland has been taken out of the EU, two years have elapsed,” she said.

“Presumably there is divergence opening up between the rules of the European Union and the single market and where the UK is going. I think it then gets much harder for Scotland to seek a different course.”

Ruth Davidson, the leader of the Scottish Conservatives, repeated her opposition to a referendum on Sunday and said it was wrong to consistently portray the Scottish National party as the voice of Scotland.

“The SNP is not Scotland and they are acting against the majority wishes of the people of Scotland in putting forward their proposition on Monday,” she said. “I’ve read far too many headlines saying, ‘Scotland reacts X, Scotland reacts Y’. No, it doesn’t. There are people right across Scotland, many, many thousands of them, that are so thankful for the prime minister to say let’s take a pause on this.

“We have asked basic questions on things like currency, on things like a central bank, on things like whether we would even rejoin Europe as a full member, and Nicola Sturgeon seems unable to commit to that.”

In a speech to the SNP conference on Saturday, Sturgeon accused the UK prime minister of “condescension and inflexibility”, insisting there would be a second referendum even if the UK government tried to block it. Holyrood is expected to back Sturgeon’s efforts in a vote on Wednesday.

Earlier on Saturday, Gordon Brown said there was an opportunity for Scotland to be granted a range of new powers after Brexit – such as more tax-raising powers, abilities to sign international treaties, and more control over agriculture, fisheries, environmental regulation, employment and energy.

An Opinium/Observer poll on Sunday found 54% of people say they believe the chances of the break-up of the UK have increased, against 16% who disagree.

When asked if they believe Scotland would choose independence if Sturgeon called a second referendum, 45% of Scottish voters said they believe the result will favour independence, with 40% predicting a vote to stay in the UK.