The Prime Minister has urged First Minister Alex Salmond to dump his plans for a two-question referendum before the next round of talks on Scottish independence take place in September.
David Cameron is said to be ready to sign off on the powers the Scottish Parliament needs for a legally binding referendum in September, provided the procedural details are arranged by then, particularly "the need for a single question".
The SNP has said it would consider adding a second option for more devolved powers – dubbed devo-max – if there was demand for it.
Speaking at a visit to Scotstoun Stadium in Glasgow, Mr Cameron said: "Frankly, the Scottish people deserve a fair, decisive and legal referendum. We've made an offer to let that happen.
"The Scottish Secretary of State and the First Minister should be hammering out the details so I can meet Alex Salmond at the end of September, and then we can go on with a date and all the rest of it. It really shouldn't be impossible to do this.
"All of the Scottish political parties from both campaigns want a one-question referendum. That's what the Scottish people deserve. Let's not let process get in the way of the outcome that the Scottish people deserve."
Scottish Secretary Michael Moore said that he hopes "this further nudge" by the Prime Minister will compel Mr Salmond to get the process sorted out by early September.
The UK Government insists that an early question is vital to give Westminster time to pass the enabling legislation, known as a section 30 order, and hand Holyrood the power it needs to hold a legally binding referendum.
If agreement is not reached soon, some politicians say they fear that the process could drag on beyond Mr Salmond's preferred date of October 2014.
Scottish Conservative leader Ruth Davidson said: "We just heard the Prime Minister say today that he's ready to sign this off in September. So let's get a move on to let Scotland know when (Alex Salmond's) going to have his referendum and that the referendum will be fair, legal and binding, and that we know who's going to vote, what the question is and that it will be a single question.
"I think people across Scotland are asking: what's the hold up and who's holding it up? At the moment the only roadblock to a referendum looks like it's Alex Salmond.
"All of the political parties in Scotland agree that it should be a single question. Both of the campaigns Yes Scotland and Better Together, believe there should be single question.
"There are elements in process that need to be hammered out and the First Minister and the Secretary of State for Scotland should be sitting down right now, making sure that these details are ironed out."
A spokesman for the First Minister said: "As we have always said, we have absolutely no objection to a Section 30 Order in regard to the referendum, with no Westminster strings attached - which could be agreed very shortly.
"The terms and timing of the referendum must be decided in Scotland, by the Scottish Parliament, not dictated by a Tory-led Government at Westminster - and the Prime Minister has already conceded the autumn 2014 timescale. We are very confident indeed of achieving a Yes vote for independence in autumn 2014.
"The Scottish Government's referendum consultation received nearly 10 times the number of responses than the UK Government consultation, and the independent analysis will be completed and published by the end of the summer.
"As the First Minister said in his letter to the Scottish Secretary last month, Bruce Crawford for the Scottish Government and Scotland Office Minister David Mundell have already had two meetings to help clarify the procedural issues which need to be considered in any wider discussions on the referendum, and they are due to meet again in August to see what further progress can be made."
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