"cite a statement" is correct and usable in written English.
You can use it when you want to refer to a specific quotation/statement. For example: "Cite a statement from the article that summarizes the main point."
Earlier in the interview, the former mayor of London appeared to mistakenly cite a statement by the Israeli prime minister, Binyamin Netanyahu, in his defence.
AMY DAVIDSON: In your piece, you cite a statement by Defense Secretary Donald Rumsfeld that the decision to remove Saddam Hussein had "nothing to do with oil, literally nothing".
Let me cite a statement made by one of the most adamant reductionists: "One feature is common to many of the transitions: entities that were capable of independent replication before the transition can replicate only as part of a larger whole after it" [ 1].
Citing an active investigation, Santa Barbara County District Attorney Joyce Dudley declined to comment, citing a statement where she credited Sacramento County District Attorney Anne Marie Schubert for her leadership in the case.
So the Obama administration's lawyers have cited a statement that was patently false.
A report by the Associated Press, citing a statement by Iraqna, said that the kidnapped engineers were from Malawi and Madagascar.
US media cited a statement from the NSA saying it was not targeting and would not target Hollande's communications.
The wounded students from the school, Nanping City Experimental Elementary School, were in stable condition at a hospital, Xinhua said, citing a statement from the city's Communist Party office.
Saudi Arabia executed a man for practicing witchcraft and committing adultery, the state news agency said Tuesday, citing a statement from the Interior Ministry.
