He also said that if it turns out USA intelligence officials leaked it to the media, it would be "a tremendous blot" on their record.
Democratic Senator Chris Coons said on CNN: "If these allegations are true, allegations of coordination between Trump campaign officials and Russian intelligence officials, and allegations that the Russians have compromised President-elect Trump's independence, that would be truly shocking". Both claims were made in a two-page note they gave him with a report on Russian meddling in the elections.
"BuzzFeed News reporters in the US and Europe have been investigating various alleged facts in the dossier but have not verified or falsified them", the online publication wrote.
Trump said: "A thing like that should never have been written, it should never have been had and should never have been released".
"But the act of publishing the dossier in its entirety isn't journalism. That's the work of journalists in 2017, or any other year".
Still, BuzzFeed was not the first media outlet to reference the report, only the first to publish it in its entirety.
When asked about a related Tuesday CNN report which said U.S. intelligence presented Trump a synopsis based on the document, Priebus did not explicitly deny the claim, but said he personally attended Friday's meeting but did not see the memo before BuzzFeed published the document on Wednesday.
Since then, CNN reported, USA intelligence agencies have checked out the former British intelligence operative and his network, and found him credible enough to include some of the information in the presentation to Trump.
BuzzFeed's article had received more than 2.8 million views by Wednesday morning.
Trump has disputed the accusations of Russian cyber attacks during the election, but his incoming chief of staff said on Sunday that the NY businessman accepts the United States intelligence community's conclusions that Russia was responsible, and that further action may be taken against Moscow.