Used to convey what somebody has said
We already know that Xと言いました can be mean “[somebody] said X”
However, looking more deeply, just as with 行こうと思う (I’m thinking of going) and 彼は行こうと思っている (He’s thinking of going), 言う more often refers to what the first person is saying, and 言っている to what the second and third persons are saying.
So we get
I told you I can’t go tomorrow.
But for the third person:
Mr Kuroda said “I’ll take the day off tomorrow.”
this can be used with the plain form to convey the message as indirect speech, in a similar way to “they said that ……” in English.
he said he’d take the day off tomorrow.
Yes, that’s what he was saying.
Have a look at this explanation from japaneseammo.com.