Although V1 responses are driven primarily by elements within a neuron's receptive field, which subtends about 1° visual angle in parafoveal regions, previous work has shown that localized fMRI responses to visual elements reflect not only local feature encoding but also long-range pattern attributes. However, separating the response to an image feature from the response to the surrounding stimulus and studying the interactions between these two responses demands both spatial precision and signal independence, which may be challenging to attain with fMRI. The present study used 7 Tesla fMRI with 1.2-mm resolution to measure the interactions between small sinusoidal grating patches (targets) at 3° eccentricity and surrounds of various sizes and orientations to test the conditions under which localized, context-dependent fMRI responses could be predicted from either psychophysical or electrophysiological data. Targets were presented at 8%, 16%, and 32% contrast while manipulating (a) spatial extent of parallel (strongly suppressive) or orthogonal (weakly suppressive) surrounds, (b) locus of attention, (c) stimulus onset asynchrony between target and surround, and (d) blocked versus event-related design. In all experiments, the V1 fMRI signal was lower when target stimuli were flanked by parallel versus orthogonal context. Attention amplified fMRI responses to all stimuli but did not show a selective effect on central target responses or a measurable effect on orientation-dependent surround suppression. Suppression of the V1 fMRI response by parallel surrounds was stronger than predicted from psychophysics but showed a better match to previous electrophysiological reports.