Foreign Secretary James Cleverly refused to confirm that up to 10 British hostages had been taken by Hamas when asked on Sunday.
The figure was put to him on Sunday With Trevor Phillips on Sky News.
Mr Cleverly declined to give an exact number and said that the situation remained uncertain, but told the programme: “That is not an unreasonable estimate of the kind of number of people that we’re talking about.”
The Israeli Defence Forces have confirmed that 126 people were taken hostage when Hamas militants crossed the border last weekend.
Speaking on the situation in Gaza, where civilians are trying to flee south ahead of a possible Israeli offensive, the minister said the UK remains committed to offering support to British nationals.
At the moment, the Rafah border crossing from southern Gaza into Egypt, remains closed although US and UK officials are working with Egypt to open the route.
He added: “This is this is very important for the British nationals in Gaza.
“We continue to support them, we continue to update them as much as we can through text messaging and whatever other means is available.
“So we will keep supporting the British nationals in Gaza and we will keep working with the US, with the Israelis and others to try and bring this crossing into use.”
As many civilians attempt to flee, Israel has massed its troops along the Gaza border with prime minister Benjamin Netanyahu declaring that the “next stage is coming”.
The Gaza Health Ministry said 2,329 Palestinians have been killed since the fighting erupted, more than in the 2014 Gaza war, which lasted over six weeks. That makes this the deadliest of the five Gaza wars for both sides.
More than 1,300 Israelis have been killed, the vast majority of them civilians killed in Hamas’s initial assault on October 7. This is the deadliest war for Israel since the 1973 conflict with Egypt and Syria.
Israel has dropped leaflets over Gaza City in the north and renewed warnings on social media, ordering more than one million Palestinians - almost half the territory’s population - to move south.
The military says it is trying to clear civilians ahead of a major campaign against Hamas militants in the north, including in what it said are underground hideouts in Gaza City. Hamas urged people to stay in their homes.
The UN and aid groups say such a rapid exodus, along with Israel‘s complete siege of the 25-mile coastal territory, will cause untold human suffering.
The World Health Organisation said the evacuation “could be tantamount to a death sentence” for the more than 2,000 patients in northern hospitals, including newborns in incubators and people in intensive care.
Gaza’s hospitals are expected to run out of fuel for emergency generators within two days, according to the UN, which said that would endanger the lives of thousands of patients.
