The pay offer was voted for by Unison members in May and was backdated to March.
However, it was not supported by the RCN, which has now lodged a dispute with the Scottish Government and is calling for further discussions over pay.
Julie Lamberth, chair of the RCN Scotland board, wrote to health secretary Humza Yousaf on Wednesday to notify him of the dispute.
Members have “serious concerns regarding the recruitment and retention of the nursing workforce in Scotland”, she said,
She said: “The Scottish Government has relied on the good will of nursing staff for too long.
"For years, we have been responding to the challenge of delivering safe and effective patient care, in the face of increasing demands, staff shortages and low pay. These issues have been exacerbated by the pandemic.”
She added: “Today’s action - writing to the Cabinet secretary to lodge our trade dispute – is a formal expression of our members’ frustration and concern for patient safety. We are sending a clear message that the time to value nursing as a safety critical profession is now.”
Scottish Labour has supported the RCN.
Health spokesperson Jackie Baillie said: “Nicola Sturgeon has been more than happy to stand on her doorstep and clap for our nurses, but they don't need a PR stunt. What they really need is a decent pay rise.”
Health secretary Humza Yousaf labelled the action “disappointing”, and said he would be happy to meet with the union.
He told MSPs on Wednesday: “This government has an exceptional record, and these are the most unprecedented of times.
"The record pay rise that we have implemented, which is the single largest pay rise for NHS staff in a single year, comes on top of the £500 thank you payment.
"The number of qualified nurses and midwives in Scotland is at a record high, having gone up by 12.8 per cent to more than 46,000. We have 8.5 qualified nurses and midwives per 1,000 people, compared to 5.9 per 1,000 in England.”
The RCN said representatives they look forward to meeting with the health secretary.