Quick answer
Нет, спаси́бо.
nyet spasíba — and why one refusal is often not enough
The options
Нет, спаси́бо.No, thank you.
Спаси́бо, не на́до.Thanks, there’s no need.
Спаси́бо, я сыт / сыта́.Thank you, I’m full.
Мне доста́точно.That’s enough for me.
Спаси́бо, в друго́й раз.Thanks, another time.
One no is not a no
A Russian host will offer again after a first refusal, because a single нет is read as not wanting to impose. To actually stop the offers, give a reason: Спаси́бо, я сыт, Я за рулём, Мне нельзя́ сла́дкое. Reasons are accepted immediately.
Softening a refusal
Спаси́бо, не на́до is the gentlest all-purpose version. В друго́й раз (another time) keeps the door open. And Я бы с удово́льствием, но… — I’d love to, but — is the standard way to decline an invitation without offence.
What you hear back
То́чно не хоти́те?Are you sure you don’t want any?
Ну хоть немно́жко!Just a little bit!
Как хоти́те.As you wish.
Typical mistakes
Не хочу́. — on its own
Спаси́бо, не на́до.
A bare “I don’t want” sounds abrupt.
Я по́лный.
Я сыт / сыта́.
по́лный describes your build, not a full stomach.
Check yourself
Which actually stops the offers?
A concrete reason is accepted at once.