The US State Department has denied that Kerry was involved.
The whistleblower organisation had accused Ecuador of cutting Assange's Internet access a day earlier, saying "We can confirm Ecuador cut off Assange's internet access Saturday, 5pm GMT, shortly after publication of Clinton's Goldman Sachs speechs."
On Tuesday, it released another lot of emails from the Clinton campaign chairman John Podesta. None of the material released has contained any sensational disclosures.
In a tweet, WikiLeaks said yesterday: "Multiple US sources tell us John Kerry asked Ecuador to stop Assange from publishing Clinton docs during FARC peace negotiations.
"The John Kerry private meeting with Ecuador was made on the sidelines of the negotiations which took place principally on 26 September in Colombia."
BREAKING: Multiple US sources tell us John Kerry asked Ecuador to stop Assange from publishing Clinton docs during FARC peace negotiations.— WikiLeaks (@wikileaks) 18 October 2016
Colombia's rebel group FARC signed a peace deal with the country's government last month.
The office of Ecuador's foreign minister, Guillaume Long, released a message on Twitter, saying that Assange's asylum status would remain as long as the issues that led to it were unresolved.
Ecuador ratifica vigencia de asilo concedido a Julian Assange pic.twitter.com/CWvzFnNbpH— Cancillería Ecuador (@CancilleriaEc) 17 October 2016
Update: Ecuador has now issued a statement, confirming that it cut Assange's Internet access because it does not believe in interfering in elections in other countries.