A government spokesman said on Friday that they were waiting for the results of the investigation into the March kidnapping of the woman.
Tsurkov went missing after travelling to Iraq for research purposes on behalf of Princeton University, Israeli Prime Minister Benjamin Netanyahu’s office said on Wednesday.
“Elizabeth Tsurkov is still alive and we see Iraq as responsible for her fate and well being,” it announced in a statement.
Tel Aviv added that Tsurkov was being held by Kataib Hezbollah.
In a statement on Thursday evening, Kataeb Hezbollah stressed it was looking into the fate of “Zionist hostage or hostages” in the country.
Tsurkov’s mother Irena said she had not heard from her daughter in two months.
Israeli citizens are forbidden from travelling to Iraq, which is considered an enemy state.
On her personal website, Tsurkov has stated that her research aims to “understand and convey” the views and experiences of people in the Middle East and “highlight abuses by powerful actors … in the region”.
The academic has more than 78,000 followers on Twitter and appears to have last tweeted in March.
Tsurkov is also a fellow at the New Lines Institute for Strategy and Policy, a Washington, DC-based research group, as well as a contributor to the News Line Magazine based in the US capital.
The magazine has called on the United States government to help secure her release.