An approach to international relations that involves peaceful negotiations backed up by the threat of military force if needed is known as:

Big Stick Diplomacy refers to a foreign policy approach prominently associated with President Theodore Roosevelt. This strategy emphasizes the importance of negotiating peacefully while simultaneously maintaining a powerful military presence to deter potential aggressors. The essence of Big Stick Diplomacy lies in the belief that a nation can achieve its diplomatic goals more effectively if it possesses strong military capabilities that can be employed as a last resort.

This approach gained prominence in the early 20th century, particularly in U.S. foreign policy in Latin America, where it was used to enforce the Monroe Doctrine and protect American interests. The phrase "speak softly and carry a big stick" encapsulates this philosophy, suggesting that while diplomatic efforts are favored, having the capability to wield military power serves as a significant deterrent.

The other options do not accurately capture this dual approach of diplomacy combined with military readiness. Multilateral Diplomacy focuses on collaborative efforts involving multiple countries, Peace Diplomacy emphasizes non-confrontational strategies, and First Step Diplomacy suggests a more incremental approach to negotiations without the explicit threat of force.