The Westminster Magistrates Court on Tuesday considered four issues raised by Assange's lawyers relating to the warrant. The court's final ruling will be issued on 13 February.
In a statement, the Ecuador Government said: "The Ministry of Foreign Affairs and Human Mobility informs that the Government of Ecuador will maintain international protection for the citizen, Julian Assange, as long as the danger to his life persists. This decision is adopted in accordance with the constitutional mandate of the defence of human rights and international treaties on this matter signed by Ecuador."
It added that it was maintaining "the best relations" with the UK and that it would work to find a satisfactory solution to the Assange issue which respected human rights.
Summers said that the warrant had lost its purpose because Sweden had dropped its investigation in May last year.
After the hearing, his lawyers said they would continue to seek an assurance that he would not be extradited to the US before he agreed to leave the Ecuadorian embassy where he has been taking refuge since 2012, after the British government sought to extradite him to Sweden to face an investigation into the alleged rape claims.
The senior district judge and chief magistrate Emma Arbuthnot said she was "not persuaded that the warrant should be withdrawn".
Not surrendering to bail was a standalone offence under the Bail Act and Assange had to say why he had failed to do so, she said. The offence carries a maximum term of a year behind bars.
Assange's problems began when he visited Sweden in August 2010 to attend a conference where he was scheduled to give a talk. During that visit, he had sex with two women whom he met. The pair filed rape and molestation complaints against him later, claims that he denied.
He was questioned by Swedish authorities and cleared of all accusations. He could have left the country then and there but stayed for a while, in case the authorities decided to question him again.
Interpol issued a Red Notice for his arrest on 20 November 2010. On 27 November, Assange surrendered to authorities and appeared before a Westminster judge. Bail was granted to him in December after his backers provided £240,000 in cash and sureties.
Then began a protracted period of legal back and forth that went on until June 2012, when Swedish prosecutors sought his extradition.
Assange's lawyers, among them the world-renowned Australian Geoffrey Robertson, replied that if he agreed to the extradition request, then he could be flown to the US from there.
On 19 June 2012, he jumped bail and took refuge in the Ecuadorian embassy, seeking asylum in the South American country. British police surrounded the building and blocked any chance of his leaving.
Ecuador granted him asylum in August 2012. He has had to stay inside the four walls of the embassy since then. He was recently granted Ecuadorian citizenship.