Current SARS-CoV-2 vaccines provide protection for COVID-19-associated hospitalization and death, but remain inefficient at inhibiting initial infection and transmission. Despite updated booster formulations, breakthrough infections and reinfections from emerging SARS-CoV-2 variants are common. Intranasal vaccination to elicit mucosal immunity at the site of infection can improve the performance of respiratory virus vaccines. We developed SARS-CoV-2 M2SR, a dual SARS-CoV-2 and influenza vaccine candidate, employing our live intranasal M2-deficient single replication (M2SR) influenza vector expressing the receptor binding domain (RBD) of the SARS-CoV-2 Spike protein of the prototype strain, first reported in January 2020. The intranasal vaccination of mice with this dual vaccine elicits both high serum IgG and mucosal IgA titers to RBD. Sera from inoculated mice show that vaccinated mice develop neutralizing SARS-CoV-2 antibody titers against the prototype and Delta virus strains, which are considered to be sufficient to protect against viral infection. Moreover, SARS-CoV-2 M2SR elicited cross-reactive serum and mucosal antibodies to the Omicron BA.4/BA.5 variant. The SARS-CoV-2 M2SR vaccine also maintained strong immune responses to influenza A with high titers of anti H3 serum IgG and hemagglutination inhibition (HAI) antibody titers corresponding to those seen from the control M2SR vector alone. With a proven safety record and robust immunological profile in humans that includes mucosal immunity, the M2SR influenza viral vector expressing key SARS-CoV-2 antigens could provide more efficient protection against influenza and SARS-CoV-2 variants.