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 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."