It comes after the Unite union called off planned work-to-rule by its members in the Scottish Ambulance Service and the GMB suspended a 26-hour strike.

Unison is recommending its members accept the £515m deal.

Health Secretary Humza Yousaf said there was "nothing left in the coffers".

The RCN had asked for at least 5% above inflation, which is currently 11.1%.

The nurses' body has confirmed two strike dates before Christmas in England, Northern Ireland and Wales.

The Scottish government said the new deal was a "record high pay offer" for frontline employees, including nurses, paramedics, allied health professionals and healthcare support staff.

Annual pay rises under the latest deal would range from a flat rate payment of £2,205 for staff in bands 1 to 4 and up to £2,660 for staff in bands 5 to 7, backdated to April.

This represents an increase of 11.3% for the lowest-paid workers and delivers an average uplift of 7.5%, a government spokesperson said.

The new offer for staff on Agenda for Change contracts also includes a review into reducing the working week from 37.5 hours to 36 hours with no loss of pay.

RCN Scotland director Colin Poolman told the BBC's Good Morning Scotland programme: "We went into what have been very complex and intense negotiations and we've received an improved offer.

"It falls short of what our members were asking for, although we do see it as a credible offer.

"It will now be for our board, who are nurses in the NHS, to initially make a decision on the next steps in relation to that offer.

"They will make the decision on whether this offer goes out to the wider membership and we will keep the members updated on the progress of that."

Mr Poolman said it would be up to the RCN board to decide whether to recommend the offer to members or not.

"[The offer] means very different things to very different people in the grades," he added.

First Minister Nicola Sturgeon and the health secretary were involved in "extensive" talks ahead of this latest proposal.

Another £35m has been put towards the latest deal to avert winter strikes in the health service.

Mr Yousaf told BBC Scotland he was "delighted to be able to table a record pay offer".

He said: "It's a great offer, it's a record offer, and I hope that nurses and other NHS staff take a look at it and realise it's a fair offer too, given the financial constraints that we're under."

The health secretary told BBC Scotland that he "would love to give an inflation-busting offer, [but] I'm not able to."

He added: "I can't go any further, so that is why this is the final offer. I think it's the best offer.

"Unison, the largest health trade union, have recognised that it's one worthy of accepting and therefore I hope other NHS staff look at the deal and, in the circumstances, agree that it's a fair one."

Mr Poolman said RCN board deliberations would take place over the next few days.

"We've got to take the government at their word," he said.

"At the negotiations, it was made very clear at the end by both the first minister and the cabinet secretary they do not believe that they can find any more resource and that this is their final offer."

He added: "These are exceptional times. It's still an offer that falls short of what were our asks.

"That's why it's important that our members make the decision on whether it's accepted or not."