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Abstract Background Access to essential medicines is a critical component of universal health coverage. However, the availability of essential medicines in Sudan isn’t well studied. As well, most Sudanese people lack health insurance, making out-of-pocket spending the primary source of drug financing. Therefore, the affordability of medicines in Sudan is questionable, with only 30% of the total population being covered by a public health service or public health insurance. We undertook this study to assess the availability and prices of essential medicines in public-sector health facilities in Khartoum state. Moreover, this study aims at assessing patients’ perceived affordability of essential medicines, and accommodation and acceptability of the public facility. Methods A cross-sectional study was carried out at 30 primary healthcare facilities’ drug dispensaries across three districts in Khartoum state. Within each Centre’s dispensary unit, a standardized checklist evaluated the availability and affordability of 21 essential medicines selected from Sudan’s national essential medicines list and assessed their storage conditions. Furthermore, 630 patients were selected from all dispensary units for an exit interview that assessed their perceived accessibility, acceptability, accommodation, and affordability of essential medicines. Data were collected through the Kobo toolbox and analyzed using SPSS version 26. Results Participants’ ratings of accessibility, affordability, accommodation, and acceptability were 3.7/5, 1.5/4, 5/6, and 5.4/6, respectively, with a 26.7% full access and weak correlation between some of the indices. The overall availability of adults and pediatric medicines was 36.8% 6.7%, respectively. Cost of a single course of treatment for 10 and 16 drugs out of the 19 drugs consumed exceeds the daily wage of insured and uninsured patients, with a median price ratio of 16.4 and 62.8, respectively. Moreover, the dispensary area conditions were found to be of good quality, yet the storerooms were not functioning in 40% of the outlets. Conclusion Patients had limited access to their needed drugs due to high prices and physical unavailability, and primary healthcare capacities are not meeting the demands of citizens. The outcomes for the patients’ access variables (accessibility, accommodation, acceptance, and affordability) are comparable to those in countries with low incomes. Ensuring access to free medicines is likely to improve patients’ satisfaction with healthcare services and reduce private expenditure on medicines, which is a long-term, sustainable way towards universal health coverage in Sudan.