By Alessandra Rizzo

LONDON (Reuters) - Britain and Ecuador should resume talks over the fate of WikiLeaks founder Julian Assange, holed up in the Ecuadorean embassy in London, as early as possible, British Foreign Secretary William Hague said on Monday.

Assange has been living in the embassy's cramped quarters since fleeing there in June to avoid extradition to Sweden where he is wanted for questioning over rape and sexual assault allegations.

Ecuador has granted asylum to Assange, but the former computer hacker faces arrest if he leaves the embassy in central London. The case has triggered a diplomatic spat between the two nations, but tensions have since eased.

"We believe that our two countries should be able to find a diplomatic solution," Hague said in a statement. "We have invited the government of Ecuador to resume, as early as possible, the discussions we have held on this matter to date."

In granting Assange asylum in August, Ecuador said it shared his fears that he could face charges in the United States over the publication in 2010 by WikiLeaks of thousands of secret U.S. diplomatic cables.

But Hague said any suggestion that Assange's human rights could be put at risk by his extradition to Sweden was "completely unfounded". He also sought to assure Ecuador that the 41-year-old Australian could not face extradition from Sweden to the United States if he faced the prospect of the death penalty or human rights violations.

Sweden would be obliged to seek Britain's consent before granting any extradition to a non-EU member, he said.

"This means that the United Kingdom could only consent to Mr Assange's onward extradition from Sweden to a third country if satisfied that extradition would be compatible with his human rights, and that there was no prospect of a death sentence being imposed or carried out," Hague said.

Assange told Ecuador's Gama television network in comments broadcast last week that he expects to wait six months to a year for a deal to free him from the embassy.

A veiled threat by Britain last month that it might enter the embassy to arrest Assange had outraged Ecuador's President Rafael Correa and fuelled the diplomatic row.

But since then, Britain has assured Ecuador that it was committed to the Vienna Convention which protects the inviolability of diplomatic premises.

"I have been consistently clear that we are not threatening the embassy of Ecuador," Hague said on Monday.

Hague met Ecuador's Vice President Lenin Moreno last Wednesday during the official's visit to London for the Paralympics.

(Editing by Janet Lawrence)