The additional Tier 1 securities convert to equity if RBS's core capital ratio falls below 7.5 percent or 8 percent. The offer is due to close on Aug. 10.

"This is another important step in the road towards becoming a much stronger, safer bank for our customers and shareholders. Improving our capital resilience has been an integral part of our plan and we are well on track to achieve this," Chief Executive Ross McEwan said in a statement.

Britain began selling its share in the bank earlier this week, raising 2.1 billion pounds ($3.3 billion) through the sale of a 5.2 percent stake in the bank.

RBS has said that it will return capital to shareholders by paying dividends or buying back shares but will not be in a position to do so until 2017.

The bank's core Tier 1 ratio, a key measure of its financial strength, rose by 80 basis points in the second quarter of 2015 to 12.3 percent.

(Reporting by Matt Scuffham; Editing by David Holmes)