The project manager is experiencing delays with two critical tasks that are to be executed...

The project manager should arrange a meeting with the functional managers of the two teams and try to reach an agreement that will resolve the conflict and enable the teams to complete their tasks. This is the best option because it addresses the issue directly, involves the parties who have the authority and responsibility to make decisions, and seeks a collaborative and constructive solution. The project manager should act as a facilitator and mediator in the meeting, and help the functional managers to identify the sources of the conflict, the interests and needs of each party, and the possible options for agreement. The project manager should also ensure that the meeting is conducted in a respectful and professional manner, and that the outcome is documented and communicated to the relevant stakeholders. References:

People in Projects, Chapter 13, Section 5: Project Manager/Functional Manager Conflict

A Guide to the Project Management Body of Knowledge (PMBOK® Guide), Chapter 13, Section 4.2.3: Conflict Management

7 Big Project Management Conflicts & Ways to Solve Them All, Section 2: Conflicting Interests of Stakeholders