WASHINGTON — A senior White House official revealed Tuesday that Israel had accepted a US offer of assistance in hunting down the killers of three teens, but warned that Israel should “be precise” and avoid an overly “heavy-handed” response to that could further destabilize the situation between Israel and the Palestinians.

The statement by White House Deputy National Security Adviser for Strategic Communication Ben Rhodes came an hour after a State Department spokesperson confirmed the US had received “many indications” that Hamas was “involved” in the kidnapping and killing of three Israeli teenagers whose bodies were discovered Monday.

Rhodes said the US has offered to provide whatever counterterror assistance they can, but did not elaborate on what the aid entailed.

Israeli and US security officials had discussed possibilities for support, but reiterated that Israel “tends to have the clearest understanding of what is taking place when it comes to issues in their neighborhood.”

“In their neighborhood they tend to have the intelligence and law enforcement resources,” he said.

“Our hearts go out to the families of the three teenagers who were found yesterday,” Rhodes told members of Washington’s foreign press corps during a rare question-and-answer session Monday afternoon. “We want to continue to support Israel in finding the perpetrators and bringing them to justice,” he said, adding that “we believe that this is done effectively through working with the Palestinian Authority.”

Rhodes also said that “there has to be an avoidance of steps that can further inflame tensions,” without initially specifying which actors – Israel, Hamas, or the Palestinian Authority’s technocratic government – must do so.

When pressed on Israel’s response to the kidnappings, murders, and continuing rocket attacks launched from the Gaza Strip into southern Israel, Rhodes warned that “Israel needs to be very careful not to be so heavy-handed in their response that they are not threatening the stability of the situation and must respect the dignity of the Palestinian people.”

Rhodes said that “generally, Israel should be precise and they should not cast a net that harms innocent Palestinians in their actions.” In recent days, Israel has faced some international criticism for the rounds of West Bank arrests in which over 400 Palestinians were detained.

At the same time, Rhodes said, “Israel clearly has a deeply held belief that they need to provide for the security of their citizens and when there are three teenagers kidnapped and killed there has to be a response.”

“Terror must be pursued and counterterror measures taken but there must be restraint on both sides,” he said

Although both Rhodes and State Department Deputy Spokeswoman Marie Harf commended Palestinian Authority President Mahmoud Abbas’s stated willingness to work with Israel in the wake of the kidnappings, Harf acknowledged that Abbas did not include Secretary of State John Kerry in a round of calls to world leaders that he reportedly made after the teens’ bodies were discovered outside of Hebron.

Harf, like Rhodes, said that the US was “encouraging restraint from both sides, from the parties, to avoid steps that now could destabilize the situation,” but also noted that the US had offered “full support” both to Israel and to the PA “to find the perpetrator to this crime and bring them to justice.”

Harf declined to comment or criticize the IAF airstrikes carried out overnight against terrorist targets in the Gaza Strip.

She did, however, tread a fine line regarding Hamas’s responsibility for the kidnapping and murders. Although administration officials have been wary of asserting a connection between Hamas and the terror attack, Harf argued Tuesday that “there are many indications pointing to Hamas’s involvement, and it is also important to note that Hamas’s leadership has publicly praised the kidnappings.”

The US, she said, was still waiting to receive more details on the investigation into the youths’ kidnapping and murder.

Israeli security officials have identified two suspects – Marwan Kawasme, 29, and Amar Abu Aysha, 32, both Hamas activists from Hebron — as responsible for the abductions.

“The investigation is still ongoing, and we want to get to the bottom of what happened here,” Harf emphasized, adding that the State Department takes the investigation “very seriously, not just for the fact that these are three teenagers that’ve been killed but also given that one’s an American,” referring to Fraenkel.

Harf then, however, conditioned her remarks by saying that “there are many indications as part of this investigation that Hamas may have been involved. I am not at this point saying they were responsible. I am not putting a specific name out there. I’m saying the investigation’s ongoing.”

White House Spokesperson Josh Earnest also talked up cooperation on Tuesday, noting that ”there was some security cooperation between the Palestinian Authority and Israel as they investigated the disappearance of these young men, as they tried to bring them home safely.”

Earnest highlighted what he described as “an important security relationship between Israel and the Palestinian Authority,” adding that “we hope that that spirit of cooperation, even in the midst of this very difficult time, will continue.”