Secondary endpoints: - All-cause mortality on days 7, 14, and 28 after treatment. - PaO2/FiO2 ratio at baseline and days 2, 4, 7, 14 and 28 after treatment. - Oxygen saturation (by standardized measurement) at baseline, daily until day 14, and on day 28 after treatment. - Time to PaO2/FiO2 ratio greater than 200 mmHg. - Subjects' clinical status on the WHO 7-point ordinal scale at baseline, daily until day 14, and on day 28 after treatment. - Time to an improvement of one category from admission on the WHO 7-point ordinal scale. - Percentage of patients that worsen at least one category on the WHO 7-point ordinal scale. - Percentage of patients that improve at least one category (maintained 48h) on the WHO 7-point ordinal scale. - Sequential Organ Failure Assessment (SOFA) scale at baseline and days 2, 4, 7, 14 and 28 after treatment. - Duration of hospitalization (days). - Duration of ICU stay (days). - Oxygen therapy-free days in the first 28 days after treatment. - Duration of supplemental oxygen. - Incidence of and duration of non-invasive and invasive mechanical ventilation in the first 28 days after treatment. - Mechanical ventilation-free days in the first 28 days after treatment. - Ventilation parameters. - Incidence of new onset pulmonary fibrosis at 3 and 12 months after treatment, based on CT scan and pulmonary function tests. - Survival at 3 and 12 months. - Cumulative incidence of Serious Adverse events (SAEs) and Grade 3 and 4 Adverse Events (AEs). - Cumulative incidence of Adverse Drug Reactions (ADR) in the experimental treatment arm. - Cumulative incidence of AEs of special interest. - Levels of analytical markers (C-Reactive Protein, lymphocyte and neutrophil counts, lymphocyte subpopulations, LDH, ferritin, D-dimer, coagulation tests and cytokines...) at baseline and days 2, 4, 7, 14 and 28 after treatment. - Other soluble and cellular biomarkers that might be involved in the course of the disease and the response to MSC.