The envoy, Amos Hochstein, was in Israel and planned to meet with Prime Minister Benjamin Netanyahu, seeking a truce in the country's war with the militant group Hezbollah.
Mexico is banking on its ability to negotiate with a deal maker like Donald J. Trump, and many officials say the country is better prepared and has more leverage than it did during his first term.
The president-elect, who built his reputation on reality television, is rounding out his second administration with Dr. Oz, Fox News hosts and a former star of "The Real World."