'reiterate again' is correct and usable in written English.
You can use it when you want to state something again, typically for emphasis. Example: I would like to reiterate again that this project needs to be completed by the end of the week.
Let me reiterate again that caveats abound in such a simple analysis.
I have said and reiterate again, it is the most serious failing in this force's history.
"But I reiterate again, I want to be in the Premier League for as long as I can.
Peterson went on to reiterate again how much he loves all his kids, and only "whoops" them because he wants them to do right.
"We reiterate again today we're going to spend $7.5 billion," Mr. Barrett said at a news briefing before the company's analysts' meeting in New York.
"I think we're all frustrated and I'll reiterate again: the thing we have to do is get better defensively," Mike D'Antoni said at Wednesday's practice as the Knicks prepared to host the Memphis Grizzlies on Thursday.
That discrepancy is something that Apple's chief executive has reiterated again and again.
He reiterated again today that Mr. Stollmann would be his Economics Minister.
Keep reiterating, again and again, that depression is not something you "admit to", it is not something you have to blush about, it is a human experience.
The prime minister's stance - which he reiterated again today at question time - was backed by the Tory frontbench, and by William Hague and Michael Portillo from the opposition backbenches.
Zardari reiterated again that he and Chief of Army Staff General Kayani get along well, although he said he was very realistic about the power of the army "given our history".
