Some suggested avoiding the issue, but while that may buy you some time, it doesn't get to the root cause.
Others suggested confronting the problem. Using a proactive problem-solving approach reframes the issues, engages others in the solution and creates opportunities for an all-around positive outcome. Yet unfortunately some conflicts are virtually unsolvable and an important part of a problem solver's role is to recognize this.
I can't tell you what to do, but I can suggest how to handle this. Most dilemmas involve deciding which is the least damaging of the alternatives. But the nasty thing with dilemmas is that making no decision is almost always worse than the most terrible outcome from any of the other options. You have to decide something to minimize the overall damage.
So first, make a call and then seek support of your decision from your senior managers. When you're "advising upward," you must succinctly lay out the facts, your interpretation of the facts and the steps leading to the decision. Then your managers can make an informed decision to support you or to suggest alternatives.
After gaining the necessary support, you have to implement the decision. It will be unpleasant and stressful, but such is the nature of the situation. As an ethical leader, you need to take responsibility for the bad and the good in your project.
If you handle a situation like this decisively, but also with empathy and consideration for others, you'll find your team's respect and support for you as a leader will be enhanced.