It also advises against all travel to areas in Israel close to the border with Gaza. This includes areas south west of Ashkelon, all areas west of Be’er Sheva and north of route 211.
Britons should also not travel to within 500m of the border with Lebanon (the ‘Blue Line’) east of Metula in the north of the country.
It comes as 20-year-old Nathanel Young, a Briton serving in the IDF, died on the Gaza border on Saturday.
Two other UK nationals - 26-year-old Jake Marlowe and photographer Dan Darlington - are also missing.
Communities minister Lee Rowley told Sky News on Monday morning: "The Foreign Office is, as it always does when there are challenges around the world, working very hard to make sure it knows where British nationals are, to provide the support that is necessary and, also, whether it is in Israel, Gaza or wherever, it is encouraging people not to travel where it's not necessary, but also supporting where it's needed."
Asked if the Foreign Office knows where British citizens are, he said: "Many, many people are going in and out of Israel every single day. I think the Foreign Office is trying to focus on where it is necessary, where their support is needed.
"Obviously there is this significant challenge at the moment with people from Israel who may be in, have been taken into Gaza. The Foreign Office and the Foreign Secretary is working very hard on ensuring that we are clear about what is happening."
Speaking to reporters at his Chequers country residence, the Prime Minister said he had spoken with Israeli PM Benjamin Netanyahu earlier on Sunday to offer the UK's ongoing support, adding: "Terrorism will not prevail."
Asked what assistance is being provided to British citizens caught up in the conflict, he told reporters: "I know that there will be families who are anxious about their loved ones.
"I want to reassure them that the Foreign Office and the Government here is in close contact with our Israeli counterparts."
The surprise terror attack by Hamas started just before before 7am on Saturday with hundreds of rockets fired out of Gaza into Israel. Netanyahu declared that the country was "at war".