Mark Antony shakes the bloody hands of the conspirators after the murder and receives reassurances from Brutus that his own life is not in danger. He pretends not to be upset, although as Casear's friend, he is deeply angry. He asks if he can speak at Caesar's funeral. Cassius opposes this idea, saying he doesn't know how this will work out. Brutus, however, is willing to allow Antony to speak, as long as he agrees not to condemn the murders, to praise Caesar and to tell the crowd he praises Caesar with the permission of the murderers. Brutus also says,

And you shall speak

In the same pulpit whereto I am going,

After my speech is ended.

With a handshake and an assurance that if the conspirators can effectively show why Caesar had to die, Antony will support their actions.  What he doesn't say, though, is that he really doesn't mean it and he's only biding his time until he has substantial troops to force them out of power.

By appearing to be friendly to the conspirators, he is able to take some focus away from himself, providing him the necessary time to recruit Octavious in seeking for some revenge.