Likud MK Yoav Kisch and Religious Zionist Party MK Orit Struck sent a letter on Sunday to Prime Minister Naftali Bennett, demanding he rescinds Michael Herzog's appointment as ambassador to the US.
MKs Kisch and Struck are heads of the Eretz Yisrael Lobby, which advocates for the expansion of settlements in the West Bank.
In the letter, the MKs claimed Herzog "actively supports the dangerous two-state solution."
"The decision [to appoint Herzog as ambassador] corresponds with the government's left-wing ideals," they added.
The Eretz Yisrael Lobby heads also claimed Herzog's appointment will give the Israeli left-wing "control over the vital Israeli-American relationship."
Last week, The Jerusalem Post broke the news that President Herzog's brother Michael Herzog was Bennett's pick as ambassador to the US. The appointment was confirmed by the prime minister on Friday.