(Reuters) - Royal Bank of Scotland Plc's securities unit will now exit its U.S. mortgage trading business after originally planning to shrink it by two-thirds.

Exiting mortgage backed-security, commercial real estate and commercial mortgage-bond sales and trading "is a necessary part of repositioning our US business," an RBS spokesman said in an emailed statement.

RBS said in May it will eliminate hundreds of jobs in the United States over the course of two years to help reduce assets ahead of new rules by the U.S. Federal Reserve.

The largest foreign banks, with $50 billion (31.88 billion pounds) or more in U.S. assets, need to set up an intermediate holding company subject to the same capital, risk management and liquidity standards as U.S. banks, the Fed said in February.

"We have made significant progress against our goals and are well ahead of plan," the RBS spokesman added.

"We continually evaluate all aspects of our business on a regular basis to ensure we are strategically positioned to deliver optimal results to our clients and shareholders."

The company plans to retain its non-mortgage asset backed securities team.