A regional military escalation is not in Israel's "best interest," White House National Security spokesman John Kirby said on Sunday, as heightening cross-border tensions between Israel and Lebanon have led to fears of an all-out war.

"We don't believe that escalating this military conflict is in their best interest," Kirby said on ABC's "This Week," adding that the United States was "saying this directly to our Israeli counterparts."

Israel and the Iran-backed Lebanese group Hezbollah have engaged in rapidly escalating cross-border exchanges, including intense rocket fire overnight at northern Israel that sent hundreds of thousands of people to bomb shelters, according to the military there.

"The tensions are much higher now than they were even just a few days ago," Kirby said.

But he added that "we still believe that there can be time and space for a diplomatic solution here and that's what we're working on."

The overnight rocket fire reached Kiryat Bialik on the edge of north Israel's biggest city Haifa, leaving a building in flames, another pockmarked with shrapnel, and vehicles incinerated.

The attacks follow a Friday air strike on Beirut that killed 45 people -- including Hezbollah commanders --  and deadly blasts of communication devices across Lebanon earlier in the week that left 39 dead and almost 3,000 wounded.

Israel has signaled its intention to turn its focus to Hezbollah after nearly a year of cross-border fire that began in October, after the Palestinian armed group Hamas launched an unprecedented raid on Israel that precipitated its war in Gaza. 

"We've been working since the beginning of this conflict, October 8th and on, to try to prevent an escalation, to prevent a broadening of this conflict there in and around Israel, but also in the region," Kirby said.

Israeli Prime Minister Benjamin Netanyahu earlier in the day vowed to return residents of northern Israel displaced by nearly a year of fighting near their homes.

An escalating war is "certainly not going to be in the best interest of all those people that Prime Minister Netanyahu says he wants to be able to send back home," Kirby said.