Inbred mouse strains differ greatly in social behaviors, making them a valuable resource to study genetic and non-genetic mechanisms underlying social deficits relevant to autism spectrum disorders. A hallmark symptom of autism is a lack of ability to understand other people's thoughts and intentions, which leads to impairments in adjusting behaviors in response to ever-changing social situations in daily life. We compared the ability of BTBR T+tf/J (BTBR), a strain with low sociability, and C57BL/6J (B6), a strain with high sociability, for their abilities to modulate responses to social cues from different partners in the reciprocal social interaction test. Results indicate that BTBR exhibited low sociability toward different partners and displayed minimal ability to modify behaviors toward different partners. In contrast, B6 showed high sociability toward different partners and was able to modify social behaviors toward different partners. Consistent results were found in two independent cohorts of different ages, and in both sexes. In the three-chambered test, high sociability in B6 and low sociability in BTBR were independent of strain of the novel mouse. Since social deficits in BTBR could potentially be caused by physical disabilities in detecting social olfactory cues, or in cognitive abilities, we tested BTBR and B6 mice on measures of olfaction and cognition. BTBR mice displayed more sniffing of social odors emitted by soiled bedding than of an odorless novel object, but failed to show a preference for a live novel mouse over a novel object. On olfactory habituation/dishabituation to a sequence of odors, BTBR displayed discrimination abilities across three non-social and two social odors. However, as compared to B6, BTBR displayed less sniff time for both non-social and social odors, and no significant dishabituation between cage odors from two different novel mouse strains, findings that will be important to investigate further. BTBR was generally normal in spatial acquisition on the Morris water maze test, but showed deficits in reversal learning. Time spent freezing on contextual and cued fear conditioning was lower in BTBR than in B6. Our findings suggest that BTBR has poor abilities to modulate its responses to different social partners, which may be analogous to social cognition deficits in autism, adding to the value of this strain as a mouse model of autism.