The US and its allies are warning the Lebanese militant group Hezbollah against escalating the conflict in Israel as the US prepositions military assets to deter a potential widening of the war, multiple US officials and people briefed on the discussions tell CNN.

Senior administration officials do not believe at this point that Hezbollah is likely to join Hamas’ war in force against Israel, and officials think the warnings are having an impact even though there have been some escalation on the border.

The US is sending the message to Hezbollah to stay out of the conflict through a number of channels, including the Lebanese government and the Hezbollah-allied Speaker of Lebanon’s Parliament, Nabih Berri. Berri was mentioned by administration officials briefing Congress on Sunday as a go-between, according to a person familiar with the briefing. The US won’t officially engage with what has been designated a terrorist group, so Berri is one natural conduit.

France has also conveyed to Hezbollah, at Israel’s request, that they must stay out of the war and not escalate further or Israel will respond significantly, a source briefed on the talks said. Those discussions were also coordinated with the US, the source said.

“Western allies who have informal ties with Hezbollah have conveyed some messages,” a Western diplomat confirmed, adding that the response by Hezbollah indicated “the pre-existing will of Hezbollah not to escalate for now.”