The correct answer is D. He assured me that I need not worry.
The other options are incorrect because they do not accurately reflect the meaning of the original sentence.
In option A, the speaker is saying that he does not need to worry. However, the original sentence says that the listener does not need to worry.
In option B, the speaker is saying that the listener will not need to worry in the future. However, the original sentence does not make any predictions about the future.
In option C, the speaker is saying that you (the listener) need not worry. However, the original sentence does not use the second person pronoun “you.”
Therefore, the correct answer is D. He assured me that I need not worry. This option accurately reflects the meaning of the original sentence, which is that the speaker is trying to reassure the listener that there is no need to worry.