@Needs native check

It's OK. This order puts accent on the word "меня" (любил именно меня, а не кого-то другого) while "Он сказал, что он меня любил." puts accent on the word "любил".

If I'm not mistaken, according to the original, isn't it:
Он сказал, что он меня любит.*

I mean, indeed, he said that in the past, but at that time he was loving me, so can we (should we) use the present tense in Russian, in the second proposition? Is it customary in Russian?

Thank you! I changed it and put the accent on the любил. :)

2Eldad
Unfortunately, I don't understand the original version, but indirect English translations tell me that, all the same, it most likely should be "Он сказал, что любит меня". :-)
In Russian "он сказал, что любит" and "он сказал, что любил" are both possible and not equal in meaning.

hmm I think the Spanish sentence can refer to both "he told me he loved me then" and "he told me he loved me in the past, even if he no longer does".

Aha. OK, then my comment is not relevant here.
I read the French, and I got the impression that he told her he loved her (at that moment).

@Dima,
By "Он сказал, что он меня любит." I meant to suggest that he told me he loved me at that time (and not in the past).

Is the second "он" unnecessary here in the Russian? Should we say:

Он сказал, что меня любит.
?

In Russian both clauses of complex or compound sentence are quite independent in sense of tense. Let's add some auxiliary words to make it look more distinct. (Sorry if my English sentences are not grammatical. :-))
"Вчера он сказал, что когда-то любил меня." ~ "He said yesterday that he used to love me once."
"Вчера он сказал, что по-прежнему любит меня." ~ "He said yesterday that he loved me as before."

Yes, Eldad, the second "он" is excessive here. Usually, it's better to omit subjects in subordinate clauses if it coincides with the on of main clause. And, in general, it's a good idea to not repear the same words too often. :-) Though, some word reordering might be necessary. "Он сказал, что любит меня." sounds more natural than "Он сказал, что меня любит."

Thank you very much.

Now I know why certain sentences in Esperanto, written by Russian speakers, sound strange ;-) They omit the pronoun in the subordinate clauses - however, in Esperanto you have to retain them, as Esperanto doesn't conjugate the verb (it's the same conjugation for all pronouns), so in order to know the subject of the verb, you have to include it.

I forgot to enclose an example sentence:

[Some] Russian speakers write:
Li diris, ke amas min.

But it should be: Li diris, ke *li* amas min.

The Spanish sentence is "Он сказал, что любит меня."

I see! :-) It seems that we're dealing with stereotype thinking here :-)
btw, in Japanese it's sometimes possible to omit almost all parts of sentence except a predicate :-)

Все дело опять в согласовании времен. Во второй части предложения и в испанском, и во французском, и в немецком - прошедшее время. В русском должно быть настоящее. Потому что нам времена согласовывать необязательно :)

Ok, ok, I change it.

Ну, нам не то чтобы необязательно согласовывать времена, на просто нет нужды это делать, я бы сказал :-) Но вот на аспекты глаголов обращать внимание надо более пристальное. :-)

Ну да. А у них все четко: в каком времени говоришь, в таком и любишь )