Its calls for democratic politics have placed Arab monarchs and life-time presidents in fear of losing their power.
Qatar will track down and prosecute the perpetrators, the statement continued.
Qatar's Foreign Minister said early Wednesday that he did not make any statement regarding withdrawal or eviction of five Arab ambassadors from Doha, Al Arabiya News Channel has reported.
Mr al-Thani was quoted as saying "there is no wisdom in harbouring hostility towards Iran" and that relations with the Trump administration are "tense" despite a positive meeting between the two leaders in Riyadh, the Saudi Arabia capital, last week.
This came among other statements published on QNA, but was later denied by Qatar, stating that the website was hacked. They included calling Hamas "the legitimate representative of the Palestinian people", as well as saying Qatar had "strong relations" with Iran and the United States.
"The state of Qatar has been surprised by the actions of certain media outlets and satellite channels", the Foreign Ministry said in a Wednesday statement.
The United Arab Emirates (UAE) and the Kingdom of Saudi Arabia blocked access to the Al-Jazeera website on Wednesday, in response to statements published on QNA, the official Qatari News Agency, reporting that Qatar ordered the withdrawal of its ambassador from Saudi Arabia, the UAE, Egypt, and Bahrain.
Sheikh Saif Bin Ahmed Al Thani, the director of the Qatari government's communications office, also issued a statement, saying authorities had launched an investigation. Egypt, the UAE and Bahrain should reconsider their antagonistic stance against Qatar. Al Jazeera says it is an independent news service giving a voice to everyone in the region.
Commenting on QAD's 17th Graduation Ceremony, Buthaina Ali al-Nuaimi, president of PUE, QF, said: "Since it was founded in 1996 by HH Sheikh Hamad bin Khalifa al-Thani, the Father Emir, and HH Sheikha Moza bint Nasser, chairperson of Qatar Foundation for Education, Science and Community Development, Qatar Academy Doha has provided comprehensive and internationally recognised academic programmes".
The incident happened days after Qatar complained it was the target of "an orchestrated barrage" of criticism by unknown parties, in the run-up to Trump's visit, that alleged that the Gulf state supported militant groups in the Middle East.
There has been no comment from the UAE or Saudi Arabia.
Qatar has been at odds with Gulf states for sometime over the extent of its support for the Muslim Brotherhood, an issue that has been brought into sharper relief by Trump's demand for Gulf states to do more to fight extremism.