Australian Federal Police is investigating the claim and/or whether young people have been radicalised online and are being encouraged to commit the acts.
Cars have been set alight, a synagogue burnt down, anti-Semitic slurs painted on buildings and cars, and on Tuesday, a childcare centre close to a place of worship was set ablaze after hateful graffiti was sprayed onto its walls.
Senator Paterson said the public was entitled to more information from Prime Minister Anthony Albanese on the allegations and what action the government was taking in response.
"It's a gravely serious claim for the Australian Federal Police to make," he told ABC radio on Wednesday.
"This either means ... if it is confirmed, that a transnational terrorist organisation is sponsoring attacks in Australia, or potentially that a foreign government is engaging in state sponsored terror targeting the Jewish community.Â
"A lot more information is required about this claim, and a lot more comfort, and needs to be given about what is being done in response to it, you cannot put information out this partially, as has been done so far."
The comments come with NSW police charging a 33-year-old man over his alleged role in the spray-painting of swastikas on and an attempted arson attack upon a synagogue in Sydney on January 11.
Three men have already been charged by strike force police after vehicles and buildings were damaged in the eastern Sydney suburb of Woollahra, four more have been charged after two suspicious fires in Bondi, and another has been charged after a second vandalism incident in Woollahra.
Mr Albanese visited the Only About Children centre in Sydney's east and decried the incident as a "despicable and horrifying crime" before bowing to pressure and convening a national cabinet meeting to address attacks aimed at the Jewish community.
Leaders have agreed to establish a national database to track anti-Semitic incidents and reaffirmed their commitment to stamping out the hate crimes.
Vice-chancellors from the University of Sydney, the Australian National University, the University of Queensland and Western Sydney University, alongside members of the student and educators' unions will front a federal inquiry on anti-Semitism when it resumes on Wednesday.
With university students set to return in a matter of weeks, the institutions have acknowledged an increase in anti-Semitism and committed to prevent its occurrence on campus with education and disclosure initiatives.
"We support freedom of speech but draw the line at hate speech," Western Sydney University's submission said.
Opposition Leader Peter Dutton has repeatedly criticised the government for its handling of anti-Semitism and has suggested those who commit terrorism offences or display hate symbols be sentenced to mandatory jail time, despite concerns from legal experts.
The Australian Human Rights Commission has noted that Australia has international human rights obligations to promote equality and freedom from discrimination and protect freedom of expression.
Its submission to the federal inquiry pointed to recommendations from a United Nations committee that calls for governments to consider the content, form and objective of speech - alongside the political climate it was disseminated - when determining whether conduct should be declared an offence punishable by law.
