National security adviser Jake Sullivan on Sunday warned that Hezbollah militants pose a "real risk of escalation" at Israel's northern border. 

Sullivan, making the rounds on several Sunday TV news shows, also noted Iran's possible involvement, as the regime has long bolstered the Hezbollah terror group in Lebanon. 

"We are concerned. We see a real risk of escalation on the northern border," he told ABC's "This Week." "And that is why President Biden has been so clear and forceful in saying that no state and no group should seek to exploit this situation to their advantage or should escalate the conflict. And in fact, he has now sent the USS Eisenhower from the United States toward the region to give additional capacity to respond to any contingency and also to send a clear message of deterrence that no one should get involved in this, no one should escalate this."

"We don't have some specific new intelligence that the threat is different today from yesterday. The threat yesterday was real. The threat today is real. There is a risk of an escalation of this conflict, the opening of a second front in the north and, of course, of Iran's involvement," Sullivan added during his appearance on CBS "Face The Nation." 

HEZBOLLAH TAKES RESPONSIBILITY FOR ATTACKS ON ISRAELI MILITARY POSTS ALONG LEBANON BORDER

Cross-border clashes between armed factions in Lebanon and Israel intensified Sunday, with the Hezbollah terrorist group firing rockets and Israeli forces responding with shelling.

The Israeli army also reported a shooting at one of its border posts. The fighting has killed at least one person on the Israeli side and wounded several on both sides of the border.

Iran-backed Hezbollah, an ally of Gaza's Hamas rulers and longtime enemy of Israel, said in a statement that it had fired rockets toward an Israeli military position in the northern border town Shtula in retaliation for Israeli shelling that killed Reuters videographer Issam Abdallah on Friday and two Lebanese civilians on Saturday.

However, Hezbollah spokeswoman Rana Sahili said Sunday's increase in the intensity of the exchanges with Israel doesn't indicate Hezbollah has decided to fully enter into the Hamas-Israel war, according to The Associated Press. The fighting on the border is "only skirmishes" and represents a "warning," she said.

Sullivan also spoke about efforts to get Americans out of Gaza, noting how "Hamas has intervened" in some cases to prevent Palestinians, Palestinian Americans and others from being able to travel across the border to Egypt. In an appearance on CNN's "State of the Union," Sullivan vowed Biden "will make hard decisions to get American hostages home." 

He denied Hamas' idea of a potential prisoner swap was under active consideration by the U.S., saying the Biden administration's "focus is on working through those third country channels."

"For President Biden, they are a priority," Sullivan said. "They're the highest possible priority. And he has sent hostage experts to coordinate and consult with the Israeli government on hostage recovery efforts. He's also made sure that our diplomats are in touch with third countries in the region to explore avenues for their safe release. I have to be cautious about how much I can say about certain efforts he's undertaking, because we want to protect those efforts to give us the best possible chance of getting our people home."

"One important point when it comes to the issue of the Navy SEALs is we do not at this point have pinpoint location information for where the American hostages are," Sullivan told CNN host Jake Tapper. "So we have to continue to refine our understanding of where they are and even Jake, who they are, because we know there are 15 unaccounted for Americans, but we cannot confirm the precise number of American hostages being held by Hamas at this time." 

HEZBOLLAH WATCHES ON AS GAZA WAR SPARKS FEAR OF ADDITIONAL FRONTS FOR ISRAEL TO DEFEND

Sullivan told CBS the U.S. is also focused on the broader civilian population of Gaza, "because the vast majority of Palestinians in Gaza have nothing to do with Hamas, that they can get to safe areas, that they can get access to food, water, medicine, shelter, and that they can be protected from the fighting as it intensifies and as a potential ground operation moves forward." 

"Gaza being governed by a brutal and vicious terrorist organization is not just a challenge for the state of Israel. It's a challenge for the Palestinian people because Hamas does not represent their highest aspirations," Sullivan said. "Hamas is not looking out for… one iota about their welfare and well-being. So the Palestinian people in Gaza do deserve a leadership that allows them to live in peace and dignity and security." 

Biden’s national security adviser said the U.S. was not "making requests or demands of Israel with respect to its military operations," adding that the administration was "simply stating our basic principles – the principles upon which this country is based and all democracies, including Israel, are based. It’s what makes us different from the terrorists, that in fact we respect civilian life." He said the U.S. was not "not interfering in their military planning" or giving them any specific instructions. 

The Associated Press contributed to this report.