I'm not sure. החליט לא להגיב is grammatical, but in the news they would always say החליט שלא להגיב. I think it's a fixed expression.
Both forms are correct, without the ש the sentence is simpler, and counted as a lower Hebrew level. For that reason, if you watch the news you would hear the sentence with the ש, but if you speak with friends it may probably be omitted or not.
The imperfect could be used in this sentence too, right? I.e., החליט שלא יגיב.
It is possible grammatically, but it is just not the given sentence: he would not react means הוא לא יגיב, to react means להגיב... It is exactly the same as in English - it is possible to say either 'the PM decided he would not react' - meaning רה"מ החליט ש(הוא )לא יגיב - or 'the PM decided not to react' - meaning רה"מ החליט (ש)לא להגיב