The impasse follows one of the most politically fractured periods in Israeli politics. From 2019 to 2022 there were five separate elections as Netanyahu and his rivals struggled time and again to co-operate.
Those pledges are the main obstacle in front of Eisenkot. He and every member of his bloc bar one has previously refused to enter government with Arab parties, although there has been speculation that an agreement could be reached.
The president has broad discretion to pick the person believed to have the best chance of building a coalition and does not have to choose the leader of the party with the most seats.
Herzog began consultations with the parties after the election deadlock, looking for a route to a government that could hold.
All but one of the Jewish parties pledged before the polls not to work with Arab parties to form a government.
Eisenkot will now have 28 days to try to form a new administration, with a potential 14-day extension.
Israel's president said he would task opposition leader Gadi Eisenkot with forming a new coalition government after last week's election left neither side with a majority. During his consultations, Herzog said that preventing another election and building a stable government required factions to accept limits on what they had promised.
President Herzog said that, after consulting all parties during the week, he would give Eisenkot the first chance to form a government. He expected"factions and their representatives to understand that, in the current reality, not every commitment and promise can be fulfilled".