What message does Mark Antony's servant bring to Brutus in Act 3, Scene 1 of Julius Caesar?

After Caesar's assassination there is considerable confusion among the citizens and among the assassins themselves. There was a great deal of planning going into the plot against Caesar, but Shakespeare makes it plain that little planning went into what would happen afterwards. The biggest immediate problem seems to be to restore order. The situation is described succinctly in the following dialogue.

CASSIUS
Where is Antony?

TREBONIUS
Fled to his house, amazed.
Men, wives, and children stare, cry out, and run,
As it were doomsday.

Antony fears for his own life, since he was Caesar's best friend and right-hand man. Cassius is probably inquiring about him because he would like him killed. Antony very wisely sends a servant to Brutus, knowing that his best chance is to deal directly with the man he knows to be benevolent and honorable. The servant has evidently rehearsed the message Antony has instructed him to deliver verbally.

"Brutus is noble, wise, valiant, and honest.
Caesar was mighty, bold, royal, and loving.
Say I love Brutus, and I honor him.
Say I feared Caesar, honored him, and loved him.
If Brutus will vouchsafe that Antony
May safely come to him and be resolved
How Caesar hath deserved to lie in death,
Mark Antony shall not love Caesar dead
So well as Brutus living, but will follow
The fortunes and affairs of noble Brutus
Through the hazards of this untrod state
With all true faith."

He flatters Brutus shamelessly and makes it clear in his message that he is ready to offer him the same allegiance he had previously given to Caesar--but he stipulates that he will do so only if Brutus can justify the assassination of Caesar. Antony probably doesn't care in the least about the reasons behind the assassination, but he is trying to make it look as if he is sincere about wanting to establish permanent friendly relations with these men who have grabbed power through their bloody coup. Antony's intentions are, first, to save his own skin and, second, to find some means to overthrow Brutus and Cassius by turning the people against them. Antony is being totally dishonest and dishonorable--but he is in a perilous position.

When Antony appears, he does not insist on explanations but  offers to shake the bloody hands of each of the conspirators. Then, once again, he pretends he is more than willing to be lifelong friends with all of them if they can provide a rational explanation for their deed.

Friends am I with you all, and love you all
Upon this hope: that you will give me reasons
Why and wherein Caesar was dangerous.

Then, after seeming to reassure all the conspirators about his harmlessness, Antony brings up the request he has had in mind all along.

And am, moreover, suitor that I may
Produce his body to the marketplace,
And in the pulpit, as becomes a friend,
Speak in the order of his funeral.

When Antony is left alone with Caesar's body, his true feelings come out in a magnificent soliloquy which serves as a prelude to his famous funeral oration. The soliloquy begins:

O pardon me, thou bleeding piece of earth,
That I am meek and gentle with these butchers.

It ends with:

And Caesar's spirit, ranging for revenge,
With Ate by his side come hot from hell,
Shall in these confines with a monarch's voice
Cry "havoc!" and let slip the dogs of war,
That this foul deed shall smell above the earth
With carrion men, groaning for burial.

There is quite a contrast between this speech and the humble, conciliatory message delivered by Antony's prostrate servant.

In Julius Caesar, what message does Antony's servant deliver to Brutus?

I suspect you are referring to Act III, scene i, just after the Conspirators have murdered Caesar.  Antony has made himself scare and sends his servant ahead of him to ask the Conspirators if he might speak with them.  There is no letter, that I can see, involved.  Also, when you say "he," I'm assuming that you mean the servant, but will also look at what Antony says upon his entrance into the scene at line 147.

Here is the upshot of the servants words:

Thus, Brutus, did my master bid me kneel,
Thus did Mark Antony bid me fall down,
And, being prostrate, thus he bade me say. . .
Say I love Brutus and I honor him;
Say I fear'd Caesar, honor'd him, and loved him.
If Brutus will vouchsafe that Antony
May safely come to him and be resolved
How Caesar hath deserved to lie in death,
Mark Antony shall not love Caesar dead
So well as Brutus living, but will follow
The fortunes and affairs of noble Brutus
Thorough the hazards of this untrod state
With all true faith. So says my master Antony.

So Antony, by way of his servant, says a few things.  First he directs the servant to prostrate himself before Brutus, something one would usually do before royalty.  In this way, he flatters Brutus as a "kingly" figure.  The servant then describes how Antony loved Caesar, but will devote himself to Brutus and his cause if the Conspirators can satisfy him as to why Caesar "deserved to lie in death."  In effect, he pledges to be a loyal follower of Brutus as he was a loyal follower of Caesar.  The rest of the play and history lets us know that this is simply not true.  It must be a ruse, a ploy, and part of Antony's scheme to overcome the Conspirators and gain power himself.

Upon his entrance after Brutus and Cassius agree to hear Antony, he has a speech in which he bids goodbye to Caesar and all but dares the Conspirators to kill him also if they wish, saying:

I do beseech ye, if you bear me hard,
Now, whilst your purpled hands do reek and smoke,
Fulfill your pleasure. Live a thousand years,
I shall not find myself so apt to die.

When they do not, Antony proceeds to "bloody" his own hands by shaking the bloody hand of each conspirator, all the while plotting his own ascension and revolt against Brutus and his co-conspirators.

For more on Antony and this scene, please follow the links below.