HONG KONG/SINGAPORE, July 26 (Reuters) - Cryptocurrencies popped to the top of recent ranges on Monday as short sellers bailed out in the wake of a strong week and while traders hoped a handful of positive comments from influential investors might signal a turnaround in fragile sentiment. Bitcoin rose as far as 12.5% to hit $39,850, its highest since mid-June during the Asia session, while ether hit a three-week peak of $2,344. On the heels of bitcoin"s best week in almost three months, the move put the squeeze on short sellers. Last week, cryptocurrency enthusiast and Tesla (TSLA.O) boss Elon Musk said the carmarker would likely resume accepting bitcoin once it conducts due diligence on its energy use. It had suspended such payments in May, contributing to a sharp crypto selloff. read more Twitter (TWTR.N) boss Jack Dorsey also said last week that the digital currency is a "big part" of the social media firm"s future and, on Sunday, London"s City A.M. newspaper reported - citing an un-named "insider" - that Amazon is looking to accept bitcoin payments by year"s end. read more Brokers said that taken together the remarks were enough to finally lift the market from the floor of support where it has held steady since a May plunge, while data also pointed to heavy short-seller liquidations - suggesting many might have given up. "Over the last five trading sessions we"ve seen general near-term bullishness in the market, driven by key technicals, as well as recent positive comments," said Ryan Rabaglia, global head of trading at digital asset platform OSL. "With a record $1.2 billion in shorts liquidated over the past 24 hours, the outlook and momentum for the week ahead is positive," he said. Bitcoin was last up 8% at $38,064, putting it within sight of resistance around June"s $41,341.57 peak just a week after it was testing support at $29,500. Ether was last up 5% at $2,304.