Idk if you’re a native speaker or not, but as a native speaker of American English there is absolutely nothing wrong with this to me. You could put it in about 4 different places:
On Thursday the press freedom group Reporters Without Borders announced ____.
The press freedom group Reporters Without Borders on Thursday announced ____.
The press freedom group Reporters Without Borders announced on Thursday that ____.
The press freedom group Reporters Without Borders announced ____ on Thursday.
The first one typically has a comma after “Thursday”. The second one you could offset “on Thursday” with commas. The third one is at best really awkward without a “that” or a question word (who, what, where, why, how) and you could offset “on Thursday” with commas; you can also drop the “on”, in which case you can’t use commas. The last one is possible but could be ambiguous (it could be that “on Thursday” is part of their announcement).
