Downing Street has criticised US Secretary of State John Kerry for calling the Netanyahu government the "most right-wing in Israel's history".
A spokesman for Prime Minister Theresa May said it was "not appropriate" to attack the make-up of a democratically-elected government of an ally.
Mr Kerry has also warned Israeli policy makes a two-state solution less likely.
Tory MP Crispin Blunt said he was unsure about the UK's intervention as Mr Kerry had been "on the money".
Mr Blunt, chair of the Commons foreign affairs committee, said on its current path Israel could not stay "democratic and Jewish".
The dispute follows a US decision not to veto a UN Security Council motion criticising Israel's policy of building settlements on land occupied since 1967.
The UK voted for the resolution, and Mrs May's spokesman agreed with Mr Kerry that "the only way to a lasting peace in the Middle East is through a two-state solution".
But he said the settlements were "far from the only problem", citing the ever-present threat of terrorism that the Israeli people had had to live with.
The spokesman added: "We do not, therefore, believe that the way to negotiate peace is by focusing on only one issue, in this case the construction of settlements, when clearly the conflict between the Israelis and Palestinians is so deeply complex.
"And we do not believe that it is appropriate to attack the composition of the democratically-elected government of an ally."
The US state department said it was "surprised" by the UK's response.
A spokesman said Mr Kerry's remarks were "in line with the UK's own longstanding policy and its vote at the United Nations last week", adding that the US stance had been welcomed by Germany, France, Canada, Turkey as well as a number of Gulf nations.
President-elect Donald Trump, who will take office next month, has been critical of the current administration's Middle East policy, tweeting earlier this week that Israel had been treated with "disdain" by the US in recent years.
The UK is hoping to build a strong relationship with the new Republican administration.
Earlier this week, the UK's ambassador to Washington Sir Kim Darroch suggested Mrs May and Mr Trump would aim to "build on the legacy" of Margaret Thatcher and Ronald Reagan, who were close allies in international affairs during the 1980s and developed a strong personal friendship.
But Mr Blunt defended Mr Kerry's efforts over the past four years at brokering a lasting peace in the long-running Arab-Israeli conflict and suggested Downing Street had been making a "narrow point".
"I have absolutely no idea what was behind Number 10 briefing in the way that they did," he told BBC Radio 4's World At One.
"My only concern is it would seem to indicate that there might be something wrong with John Kerry's analysis in their view. In my judgment there isn't, it was an extremely fine speech.
"On the substance, and finding a long-term solution that's in the interests of the people of Israel and peace for her Arab neighbours and a solution that beings justice for the Palestinians and security for the Israelis, Kerry's analysis is very hard to gainsay."
A row broke out between the US administration and Israel after the vote at the UN Security Council last Friday, as Mr Netanyahu accused Washington of complicity in drawing up the resolution.
In a speech on Wednesday, Mr Kerry said Mr Netanyahu's "public support" for a two-state solution, including the creation of an independent state of Palestine, did not reflect the views of the most extreme members of his government.
"His current coalition is the most right-wing in Israeli history with an agenda driven by the most extreme elements," he said.
"The result is that policies of this government, which the prime minister himself just described as more committed to settlements than any in Israel's history, are leading in the opposite direction [from a two-state solution]. They are leading towards one state."
Mr Netanyahu said the comments "paid lip service to the unremitting Palestinian campaign of terrorism" against Israel.