The US president says it is "another in a very long line of National Security reasons why Greenland has to be acquired".
Critics of the project - including some Labour MPs - warn it could pose a security risk.
Nearly a quarter of hospital trusts in England have seen waiting times deteriorate in the past year.
Official figures show that the pace of private sector wage growth slowed to the lowest rate in five years.
The operation follows a change of tactics agreed amid growing pressure from the UK government to step up interventions.