(Reuters) - Germany is extremely concerned about rising violence on Israel's border with Lebanon and the growing risk of a full-blown regional conflict, Foreign Minister Annalena Baerbock said on a visit to the region on Monday.

Speaking at a security conference, Baerbock also warned, as a "friend" to Israel, that it could "lose itself" in the war against Hamas and that rising anger at the plight of civilians in Gaza undermined Israel's security. 

Fears are growing that a war that has already killed tens of thousands in Gaza could spill into neighbouring countries.

Prime Minister Benjamin Netanyahu signalled on Sunday that Israel could move more troops to the north, where fighting against the Iranian-backed Hezbollah militia has escalated on the border with Lebanon.

Hezbollah began trading fire with Israel on Oct. 8, a day after its Palestinian ally Hamas, which administers Gaza, attacked southern Israel, sparking the Gaza war. Tens of thousands have fled both sides of the border.  

"We are extremely concerned about the increase in violence at the northern border. I will pay a visit to Beirut tomorrow again exactly for this reason," Baerbock said, according to prepared remarks. 

"Together with our partners, we are working hard on finding solutions that can prevent more suffering. The risk of an unintended escalation and of all-out war is growing by the day."

Germany feels a historic responsibility towards Israel in a desire to atone for the genocide of Europe's Jews in the Nazi Holocaust. 

But as in other Western countries, the war in Gaza has stirred popular opposition as the Palestinian death toll - now over 37,600 - has mounted, and Chancellor Olaf Scholz's government has sharpened its rhetoric about Israel's conduct. 

Baerbock highlighted the humanitarian situation in Gaza, saying at least 17,000 children there were orphaned or separated from their parents. 

She flagged reports of human rights violations including the torture of detainees, and extremist settlers driving Palestinians from their homes in the West Bank. 

"We don't want Hamas' strategy to succeed," she said. "And we don't want Israel to lose itself in this war. What it is and what it stands for".

Images from Gaza have sparked disbelief, sadness and anger, she warned. 

"And as a friend of Israel, I want to be frank: This anger is not helping Israel to meet its security needs, to the contrary. It only serves Hamas' cynical drive to provoke further escalation."

Israel's campaign in Gaza was triggered when Hamas-led militants killed around 1,200 people in southern Israel and seized more than 250 hostages, according to Israeli tallies.

The Israeli military has said it is investigating allegations of mistreatment of detainees. A number of countries, including the United States, have imposed sanctions on violent Jewish settlers in the occupied West Bank and urged Israel to do more to stop the violence.

(Reporting by Alexander Ratz; Writing by Matthias Williams; Editing by Kevin Liffey)