His “thoughts and prayers are with all of those suffering”, Buckingham Palace says.
The King is “appalled” and condemns the “barbaric acts of terrorism in Israel”, Buckingham Palace sources say.
He has asked to be kept updated on the situation and his “thoughts and prayers are with all of those suffering”, a palace spokesman said.
The monarch is said to be “extremely concerned” about the attacks by Hamas, which began on Saturday.
Some 1,200 people have been killed in Israel, while more than 1,000 have died in retaliatory air strikes on Gaza.
The spokesman said: “This is a situation His Majesty is extremely concerned about, and he has asked to be kept actively updated.
“His thoughts and prayers are with all of those suffering, particularly those who have lost loved ones, but also those actively involved as we speak.”
Seventeen British nationals, including children, are dead or missing after the Hamas attack on Israel, an official UK source has told the BBC.
Palestinian militant group Hamas launched a series of unprecedented attacks on Israel from Gaza over the weekend, killing hundreds and taking up to 150 people hostage.
In response, Israel has launched air strikes on Gaza and prevented the passage of food, water, fuel and medicine into the territory.
More on Israel Gaza war
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- Gaza: Children screamed in street as we fled 2am air strike
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- History behind the story: The Israel-Palestinian conflict
The Archbishop of Canterbury has also condemned the “utterly abhorrent” attacks by Hamas.
In a letter to the Board of Deputies of British Jews, Justin Welby said such violence against innocent civilians including children and the elderly “strikes at the heart of all that is good and holy”.
He added that British Jews would also be feeling the “double jeopardy” of anticipating an increase in anti-semitic sentiment.
Meanwhile, Foreign Secretary James Cleverly has travelled to Israel, with the Foreign Office saying the visit was to meet survivors and outline the UK’s support for Israel.
A Foreign Office spokesperson said Mr Cleverly was in Israel “to demonstrate the UK’s unwavering solidarity with the Israeli people following Hamas’ terrorist attacks”.
British nationals Nathanel Young and Bernard Cowan have been confirmed to have died in the attacks, while the family of photographer Daniel Darlington believe him to be dead.
Jake Marlowe, who was working as a security guard at a music festival where 260 people were killed by militants, is missing.