It doesn't seem as though there is any very special relationship between the Reverend Parris and Mr. Putnam. Putnam is one of the first people to arrive at Parris's house when Betty Parris falls ill, and he is anxious to persuade Parris that witchcraft is at the root of Betty's illness as well as his own daughter, Ruth's, illness. He wants Parris to announce to the town that a witch or witches are responsible for the girls' sickness. Putnam tells Parris, "Now look you, sir. Let you strike out against the Devil, and the village will bless you for it!" He attempts to compel Parris to proclaim witchcraft by claiming that instead of it being used against Parris by his enemies, he can appear to get in front of it and take credit for his forethought.
Later in the same act, Putnam outright issues Parris an order, saying, "When Reverend Hale comes, you will proceed to look for signs of witchcraft here." He seems quite resolute, and due to his bitterness and greed, it seems possible that he may already be attempting to manipulate Parris so that he can accuse his political enemies or those whose land he desires.