Upvote:4
As far as I'm aware, the US does not officially require a letter of consent for most minor children travelling with one adult.
The reason for the Mexican/Canadian exception is that minors travelling from those countries are able to enter the US without a passport. Most countries require a minor applying for a passport to have the consent of both parents before applying (or suitable documentation as to why both parents can't consent, such as custody documentation), which is why the additional requirement exists for minors travelling without a passport.
However, even where such a letter is not officially required, it is still a VERY good idea to carry one. Entering a foreign country is always a privilege and not a right, which means that foreign immigration always has the ability to submit a traveler to additional scrutiny and even to deny them entry to a country for any reason that they see fit.
Taking a child across an international border without the consent of both parents can be deemed trafficking and/or kidnapping, so it is something that border officials do look out for. Being able to show documentation that confirms that the other parent has given consent will significantly reduce the potential for such issues when crossing any international border.