Assange took refuge at the embassy in June to avoid extradition to Sweden, where he faces questioning over assault and rape claims, which he denies.
Ecuadorian Foreign Minister Ricardo Patino also said a decision on the Wikileaks founder's asylum request would be made public at 7 a.m. Thursday, the BBC reported.
At the same time, the British Foreign Office said it could revoke the embassy's diplomatic status, and the UK had a "legal obligation" to extradite Assange.
"Under British law we can give them a weeks' notice before entering the premises and the embassy will no longer have diplomatic protection," a Foreign Office spokesman said in a statement quoted by Reuters. "But that decision has not yet been taken. We are not going to do this overnight. We want to stress that we want a diplomatically agreeable solution."
Meanwhile, a number of police officers are outside the embassy, in Knightsbridge.
At a news conference in Quito Wednesday evening alongside Assange's mother, Patino said a letter was delivered to the Ecuadorian government through a British Embassy official there.
"Today we received from the United Kingdom an express threat, in writing, that they might storm our Embassy in London if we don't hand over Julian Assange," he said. "Ecuador rejects in the most emphatic terms the explicit threat of the British official communication."
Such a threat was "improper of a democratic, civilized and rule abiding country," Patino said.
"If the measure announced in the British official communication is enacted, it will be interpreted by Ecuador as an unacceptable, unfriendly and hostile act and as an attempt against our sovereignty. It would force us to respond," he said. "We are not a British colony."
The British said they have been trying to negotiate with Ecuador, but may invoke the Diplomatic and Consular Premises Act of 1987, which allows the UK to revoke the diplomatic status of an embassy on its soil.
Ecuador, whose government is part of a left-leaning bloc of nations in South America, called for meetings of regional foreign ministers and the hemispheric Organization of American States to rally support in its complaint against Britain.
Swedish prosecutors have not yet charged Assange, but they have moved forward with their investigations and they believe they have a case to take to trial.
Assange fears Sweden could send him on to the United States, where he believes authorities want to punish him for publishing thousands of secret U.S. diplomatic cables on WikiLeaks in 2010 in a major embarrassment for Washington.