Hague said that Ecuador's decision to grant Assange political asylum should not be used as a means for him to escape the legal process in Sweden, where Assange is wanted for questioning over allegations of rape and sexual molestation.
"The United Kingdom does not recognize the principle of diplomatic asylum", Hague said in a news conference in London.
Hague said the current situation could continue for some time, but that there is no threat to storm the embassy where Assange is holed up.
US denies pressure on UK over Assange case
The United States said on Thursday that it was not pressuring Britain to seize WikiLeaks founder Julian Assange.