A method of producing a glass vessel includes holding a borosilicate glass tube with a first holding device, and holding an open end portion of the glass tube with a second holding device such that the second holding device is spaced apart from the first holding device. Heat is applied to the glass tube by a burner to separate the open end portion and form a bottom portion on the open end portion. Fire-blast treatment of an inner surface of the open end portion with a flame from a point burner is performed during at least a part of (i) applying heat to the borosilicate glass tube for separation, (ii) applying heat to the separated open end portion for bottom portion formation, and/or (iii) a period applying heat to the separated open end portion and prior to releasing the glass vessel from the second holding device.