In general, construction projects are vulnerable to various risks during their life cycle. These risks may negatively affect the project cost and duration, in addition to other factors, including environmental impact, health and safety, and quality of construction work. The COVID-19 pandemic has brought more challenges to construction projects. This study presents an assessment of 47 major risks affecting construction projects. The research investigates and assesses the risk factors associated with a special type of construction project, namely, projects funded by external sources, due to their importance, characteristics, and sensitivity. Furthermore, the study was carried out under the impact of the special conditions and constraints associated with the COVID-19 health pandemic. These conditions provided specific types of risks, results of risk assessment, and recommended responses to the risks. The studied risks were categorized using the PESTLE technique, an external factor analysis technique, which includes six groups of Political, Economic, Social, Technological, Legal, and Environmental risks. A questionnaire survey was conducted on 34 construction organizations that implemented or supervised projects funded by external sources. The aim of the survey was to assess the risks affecting the construction projects in terms of probability of occurrence and severity on the projects’ cost and time schedule. Then, the importance of each risk was calculated, and the risks were ranked according to their importance. The results showed the high importance of environmental and legal risks and indicated that the most important risk factors are the difficulty of issuing licenses and permits and the inappropriate definition of the scope of work. This study would help managers and fund providers make decisions regarding risks during uncontrolled pandemic or disastrous circumstances. Although the current study was conducted in Jordan, its procedures and results can be useful in other locations with different properties and conditions.