In evidence to the Commons foreign affairs committee he insisted there was wide support for the stance in many European capitals and dismissed the concerns of a leading business figure.
On Tuesday it was called a "very risky strategy" that will cause four years of uncertainty by the man challenging Angela Merkel to become the next German chancellor in September.
Social Democrat Peer Steinbrueck, said that treaty change would set off a string of referendums - with unpredictable consequences - across the continent. His comments came as French president Francois Hollande insisted there could be no "a la carte" Europe - a stance backed by Mr Steinbrueck after talks with Labour leader Ed Miliband
Mr Hague denied raising the prospect of withdrawal was a "threat" to other member states, saying: "It is not a threat; it is part of a vibrant and robust democracy that we have in this country."
He said he had seen no evidence that Mr Cameron's pledge had in any way lessened Britain's influence in the EU - and predicted that it could in fact increase it, adding: "We are a major player in the European Union and we make our alliances on a vast range of subjects and I do not believe our ability to do that would be diminished."