The projected cost of government-funded childcare to disadvantaged two-year-olds has risen by a third and could change again, the Education Secretary has said.

Mike Russell said the Government has already found an extra £20 million following negotiation with councils and that he is "absolutely not ruling out there being a different figure at the end of the day".

Councils say it will cost £114 million to deliver 600 hours of childcare to two-year-olds from workless households - nearly three times the Government's opening bid of £41 million.

But Mr Russell said ministers "don't agree with that figure" and insisted their present calculation of £61 million is "robust".

The Scottish Government had previously insisted that "concerns have not been raised" by councils during evidence to Holyrood's Finance Committee three months ago.

But council umbrella group Cosla has now come forward with "significant concerns with regard to the capital funding available", in a new submission to the committee.

Mr Russell said the term "no concerns" was open to interpretation when pressed on the matter by the committee today.

Responding to Cosla's claims that £61 million is "somewhat optimistic", Mr Russell said: "Well, we don't believe so.

"I'm not saying that this cannot continue to be negotiated, and of course in a negotiation both partners take robust positions and then discuss it."

SNP MSP Ken Gibson, the committee's convener, said: "How flexible are you in terms of that £61 million figure if negotiations are continuing with Cosla?"

Mr Russell said: "The Cosla figure is very substantially higher but we have moved from early discussions of a lower figure.

"We will continue to discuss it but we are confident in our robust calculations. Of course, there will be flexibility but I think these calculations are very robust indeed."

SNP MSP John Mason said: "The suggestion was made that clearly when negotiations are going on one party starts at one end and one party starts at another end, and there is a movement towards the middle.

"Is the £61 million after there has been some movement towards the middle? It's not the starting point, or is it?"

Mr Russell said: "It's not the starting point but we are in the process of negotiation.

"We are talking about the £61 million like this because we believe it is robust and well-founded.

"Clearly, Cosla has talked about £114 million but we don't agree with that figure for reasons we have also given to Cosla."

Mr Mason said: "But you have already moved from a lower figure?"

Mr Russell said: "Yes, I think we were at £41 million some time ago.

"I am absolutely not ruling out there being a different figure at the end of the day but I am saying we believe the £61 million is well-founded."

Conservative MSP Gavin Brown said: "Is the £61 million basically you taking a robust position for discussion in a negotiation?"

Mr Russell said: "Our £61 million is based upon the metrics, so I think that is a provable figure and that's the figure that we are discussing, and I think it's a well worked out set of calculations and what I believe is the right approach to this.

"But I'm not going to indicate an inflexibility because there isn't an inflexibility. We are working as partners on this and we will continue to work as partners."

Mr Brown added: "When we had evidence from the Scottish Government on February 19, they said 'we've shared our workings with Cosla and concerns have not been raised'.

"How do you explain that statement with what Cosla has said in their written submission to us, where they are quite clearly raising 'significant concerns'."

Mr Russell said: "Work has been done since then on both sides but no indication was given that there was an agreement and we have continued to try and do this in a very positive way.

"But there was no final agreement, there wasn't even an interim agreement.

"It depends on the interpretation of 'no concerns'. I think that there was a good mutual relationship and there continues to be.

"There is clearly a discussion to be had about the fine detail of paying for something."

Mr Brown said: "You're saying it's interpretation but either they had raised concerns or they hadn't."

Mr Russell said: "I think the evidence an official gives is the evidence an official gives.

"They obviously have a good positive relationship and have been discussing it. We continue to discuss it and figures have been worked on and varied since that time."

Mr Russell was standing in at the Finance Committee for children's minister Aileen Campbell, who he said was ill.

A Cosla spokesman said: "We have a number of difficulties with this.

"The first being that Mr Russell has form for talking about a negotiation with councils whist not delivering on it, a perfect example being his recent stance on rural schools.

"We have learned from previous dealings with him that his actions do not always match his words.

"That is why, if I am being honest, his meagre assurances around this policy do not cut any ice with us.

"So, unless he has had some form of conversion his attempt to work in partnership on this has to be treated with a pinch of salt.

"Another difficulty that we have is that we are also adamant that our figure from a trawl of councils is robust.

"The fact that we are in this position reinforces our concerns on delivery prior to the start of term in August, a point which we will be making to the Education Committee in the strongest possible terms later this month."