Emir of Qatar Sheikh Tamim bin Hamad Al-Thani and Turkey's President Recep Tayyip Erdogan.
The Post's story cited USA intelligence sources who said they had new information implicating UAE officials in the attacks on the Qatari government's news sites and social media.
Speaking during a trip to London, Minister of State for Foreign Affairs Anwar Gargash said the four-nation bloc led by Saudi Arabia that's isolating Qatar needs a clear signal that the emirate is willing to reexamine its position regarding extremism and terrorism.
Qatar has previously stated that its intelligence uncovered information that iPhones from countries blockading countries were involved in the false information campaign.
"The Washington Post story is not true, purely not true", he said responding to a question after a speech at Chatham House in London.
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt imposed sanctions on Qatar on June 5, cutting diplomatic and transport ties with the tiny Gulf monarchy, accusing it of financing extremist groups and allying with Gulf Arab states arch-foe Iran. It is still unclear if the USA believes the UAE carried out the hack or hired another country to do it. The false reports said that the emir, among other things, had called Iran an "Islamic power" and praised Hamas, The Washington Post reported. The fake reports spread like wildfire across neighboring Gulf states.
U.S. spies now believe those comments to have been concocted and planted on Qatari government websites.
"This is our message: You can not be part of a regional organisation dedicated to strengthening mutual security and furthering mutual interest and at the same time undermine that security", he said.
When asked whether Qatar's membership was at stake, Gargash did not answer directly and repeated his remarks.
Gargash refused to give details of any further punitive measures being planned beyond saying that financial institutions and "people being harbored and supported by Qatar" might be targeted.
Qatar has refused to comply with the 13 demands and says the list and the boycott itself are aimed at "limiting Qatar's sovereignty, and outsourcing our foreign policy".
Initially the U.S. seemed to have taken sides with them against Qatar in the dispute, President Trump accusing the Qataris of funding terrorism "at the highest level".