Russia has accused Prince Charles of making outrageous and low remarks in comparing Vladimir Putin with Adolf Hitler, as the fallout from the comments threatens to descend into a diplomatic row.

The delayed but furious response to the prince's comments came before a meeting with the Foreign Office which was demanded by the Russian embassy in London.

In a statement on Thursday, the embassy said: "The outrageous remarks made by Prince Charles in Canada will be among the questions raised. The embassy asked the FCO for official clarifications on that yesterday."

Russia's foreign ministry spokesman, Alexander Lukashevich, underlined the Kremlin's anger.

"If these words were truly spoken, then without doubt, they do not reflect well on the future British monarch," he told a news conference.

"We view the use of the western press by members of the British royal family to spread the propaganda campaign against Russia on a pressing issue – that is, the situation in Ukraine – as unacceptable, outrageous and low," he said.

The prince is reported to have made his comments during a private conversation with a Jewish survivor of the second world war about the dispute over Russia's annexation of Crimea. "Now Putin is doing just about the same as Hitler,"he told Marianne Ferguson, a volunteer at the Canadian Museum of Immigration in Halifax.

Russia's second most senior diplomat in the UK, Alexander Kramarenko, the embassy's minister counsellor, will attend the meeting with the Foreign Office later on Thursday. Russia is seeking clarification about what exactly the prince said.

A Foreign Office source said UK ministers were unlikely to get involved, and the meeting would be hosted by senior Foreign Office officials.

Russia's decision to seek the meeting suggests the Kremlin is more angered by the remarks than it had let on. Until Thursday Russian officials had not responded publicly to the remarks, and Russian TV channels had remained unusually quiet on the issue.

The popular Russian daily paper Moskovskij Komsomolets said the remarks risked "triggering an international scandal" and complicating "clouded" UK-Russian relations.

There was a mixed reaction from Britain's political leaders. Ed Miliband, the Labour leader, offered the prince some backing by claiming that many in Britain shared the prince's concern about Putin and his actions in Ukraine. David Cameron refused to be drawn on the issue. Nigel Farage, the Ukip leader, who has expressed admiration for Putin in the past, said Charles was wrong to make his views known.