In all the scriptures of Hindus there is no direct words from Bhagwan except Geeta. Only Geeta contains "Shree Bhagwan Uvachah" means "God said : " is it mean that other scriptures are human made where as Geeta is direct statements from GOD only? Geeta is at highest priority.
"Bhagvan uvacha" meaning "God spoke" is used in several texts, not only in Bhagvad Gita. There are many Puranas using "Bhagvan uvacha".
In the Mahabharat itself "Bhagvan uvacha" is used in several places other than Bhagvad Gita. "Bhagvan uvacha" is also used when Lord Shiva is speaking. Lord Shiva speaking is denoted using "Maheswara Uvacha", "Mahadeva Uvacha", "Bhagvan Uvacha" etc...
For eg. Lets take example of chapter 40 of Vana Parva where Lord Shiva in the form of Kirat goes in front of Arjuna. Here are some of the quotes from that chapter:
नरस्त्वं पूर्वदेहै वै नारायणसहायवान् ।
वदर्यां तप्तवानुग्रं तपो वर्षायुतान्बहून् ।।
Bhagvan Said: 'Thou wert in thy former life Nara, the friend of Narayana. In Vadari wert thou engaged in fierce ascetic austerities for several thousands of years.'
Then after sometime Arjuna asks weapons from Lord Shiva and at last:
एष मे प्रथम: कामो भगवन्भगनेत्रहन् ।
त्वत्प्रसाद्विनिर्वृत्तः समर्थ : स्यामहं यथा ।।
Arjuna Said: "O illustrious destroyer of the eyes of Bhaga, even this is my foremost desire, viz., that I may be able to fight with them and obtain success."
Then Lord Shiva gives Pasupatastra to Arjuna.
ददानि तेऽस्त्रं दयितमहं पाशुपतं महत् ।
समर्थो धारणे मोक्षे संहारे चापि पाण्डव ।।
नैतद्वेद महेन्द्रोऽपि न यमो न च यक्षराट् ।
वरुणो वाथ वा वायु: कुतो वेत्स्यन्ति मानवा ।।
Bhagvan Said: "O powerful one. I will give to thee that favourite weapon of mine called the Pasupata. O son of Pandu, thou art capable of holding, hurling, and withdrawing it. Neither the chief himself of the gods, nor Yama, nor the king of the Yakshas, nor Varuna, nor Vayu, knoweth it. How could men know anything of it? "
Thus as we can see from above the conversation between Arjuna and Lord Shiva is in the format of "Arjuna Uvacha" and "Bhagvan Uvacha". Thus the term "Bhagvan uvacha" is also frequently used in other places itself in the Mahabharata.
Bhagavan uvacha appears in many puranas also.
Please read them carefully, you will surely find them in many puranas. Simple e.g. is Vishnu Purana where Sri Bhagavan uvacha appears in many chapters, where Lord Vishnu is mostly addressed as Bhagavan For e.g in Book 1 of Chapter9 chapter 12( at many instances), Chapter 20. This is simple sample. Sri Bhagavan uvacha appears umpteen number of times in Vishnu Purana.