Related Rule
United States of America
Practice relating to Rule 66. Non-Hostile Contacts between the Parties to the Conflict
Section A. General
The US Field Manual (1956) states: “Absolute good faith with the enemy must be observed as a rule of conduct.” 
United States, Field Manual 27-10, The Law of Land Warfare, US Department of the Army, 18 July 1956, as modified by Change No. 1, 15 July 1976, § 49.
The manual also states:
452. One belligerent may communicate with another directly by radio, through parlementaires, or in a conference, and indirectly through a Protecting Power, a third State other than a Protecting Power, or the International Committee of the Red Cross. …
453. It is absolutely essential in all nonhostile relations that the most scrupulous good faith shall be observed by both parties, and that no advantage not intended to be given by the adversary shall be taken.
458. In current practice, radio messages to the enemy and messages dropped by aircraft are becoming increasingly important as a prelude to conversations between representatives of belligerent forces.
469. In its narrower sense, a cartel is an agreement entered into by belligerents for the exchange of prisoners of war. In its broader sense, it is any convention concluded between belligerents for the purpose of arranging or regulating certain kinds of nonhostile intercourse otherwise prohibited by reason of the existence of the war. Both parties to a cartel are in honor bound to observe its provisions with the most scrupulous care, but it is voidable by either party upon definite proof that it has been intentionally violated in an important particular by the other party. 
United States, Field Manual 27-10, The Law of Land Warfare, US Department of the Army, 18 July 1956, as modified by Change No. 1, 15 July 1976, §§ 452, 453, 458 and 469.
The US Naval Handbook (2007) states: “The [1949] Geneva Conventions recognize the special status of the ICRC and have assigned specific tasks for it to perform, including … serv[ing] as a neutral intermediary between belligerents.” 
United States, The Commander’s Handbook on the Law of Naval Operations, NWP 1-14M/MCWP 5-12.1/COMDTPUB P5800.7, issued by the Department of the Navy, Office of the Chief of Naval Operations and Headquarters, US Marine Corps, and Department of Homeland Security, US Coast Guard, July 2007, § 6.2.2.
The US Uniform Code of Military Justice (1950) punishes “any person … who communicates or corresponds with or holds any intercourse with the enemy, either directly or indirectly”. 
United States, Uniform Code of Military Justice, 1950, Article 104(2).
According to a memorandum of a legal adviser of the US Department of State in 1975, the president, as commander-in-chief of the armed forces, has the constitutional authority to conclude armistices and other agreements relating to the military security of the United States. 
United States, Legal Adviser to the Department of State, Memorandum of Law on the authority of the US President to enter into international agreements pursuant to his independent constitutional powers, 31 October 1975, reprinted in Eleanor C. McDowell, Digest of United States Practice in International Law, 1975, Department of State Publication 8865, Washington, D.C., 1976, pp. 314-315.
The Report on US Practice states:
The need to seek express authority to negotiate an agreement with the enemy … has been reinforced by the erosion, since the end of World War II, of distinctions between political agreements, such as peace treaties, and purely military agreements, such as truces and armistices … [The Air Force Pamphlet] noted that the practice of concluding peace treaties had become rare, and that armistices had often become functional substitutes for peace treaties. The term “cease fire” was increasingly used for agreements that would once have been designated armistices.
Modern combat conditions may also make it more difficult to communicate directly with an enemy armed force.
US commanders have little inherent authority to negotiate with the enemy, and unauthorized communications with the enemy may be a military offense. The practice of the United States no longer recognizes any clear category of agreements as purely military without political overtones. 
Report on US Practice, 1997, Chapter 2.2. (The report notes that general armistices often include political provisions, and therefore require high-level approval.)