The WHO's Nima Saeed Abid said technicians were unable to access the National Public Health Laboratory to secure the biological materials.
Cohen said he hoped that working to achieve calm in Sudan "would allow for the signing of a historic peace agreement."
The embassy closure comes amid a power struggle and violence, threatening democratic progress in the Sudan.
It is now clear that key countries linked to the West are all concerned that fighting may grow worse and access to basic things such as medical services and even clean water may be an issue.
Many countries have an interest in a ceasefire in Sudan yet it doesn't seem like they are willing to invest in ensuring that one holds.
Sudan's paramilitary Rapid Support Forces (RSF) had agreed to the 72-hour truce earlier in the day.
At least 270 people have died and 2,600 have been injured, the World Health Organization said, citing Sudan's health ministry.
The military and RSF, which numbers some 100,000 members, have been competing for power as political factions negotiate forming a transitional government.