Foreign Secretary David Miliband has warned Russia that "intimidation" of British Council officials is "completely unacceptable".
The council is "deeply concerned" about its staff's safety after its employees were interviewed by security services and a director was detained by police.
Mr Miliband said the Russian ambassador in London would meet the head of the diplomatic service over the issue.
"Any intimidation or questioning of officials is completely unacceptable."
The British Council says it is "deeply concerned" for the safety of its staff, after its employees in Russia were called in for interviews with the FSB security service - and some were visited by Interior Ministry officials at their homes late on Tuesday.
Meanwhile, St Petersburg office director Stephen Kinnock was followed, stopped and released by authorities on Tuesday.
Mr Kinnock - son of former Labour leader Neil - was held by the side of the road on Tuesday night and accused of going up a one-way street the wrong way and of smelling of alcohol. The British Consul in St Petersburg came to pick him up an hour later.
The St Petersburg British Council office closed on Wednesday because all Russian staff have been summoned by the Russian authorities.
The British Council has been at the centre of a row between Russia and the UK, part of an ongoing dispute over the death of ex-KGB agent Alexander Litvinenko, who was poisoned in London. Russian authorities have ordered offices outside Moscow to shut - Britain has refused.
Mr Miliband said Tuesday had seen "productive" discussions between British diplomats and Russian authorities in Moscow.
But he said: "We've also heard last night and today very serious reports of intimidation and harassment of British Council officials, obviously we take that very seriously indeed."
He said he would meet the chief executive of the British Council to discuss the matter later and the Russian ambassador would meet the head of the British diplomatic service.
Mr Kinnock was detained by police in St Petersburg
Mr Miliband argued that cultural exchange between the two countries was a good thing and that the council's work was "completely legal" and Britain would defend its staff's integrity.
And he said the only losers, should the offices shut, would be the Russian people and the reputation of the Russian government.
The British Council, which aims to promote cultural and educational ties, has been accused of violating Russian tax rules.
The row comes on top of ongoing tensions over the death of former KGB officer Mr Litvinenko in London in November 2006. He had been given a fatal dose of radioactive polonium 210.
The UK wants Russia to hand over businessman Andrei Lugovoi, whom UK investigators suspect of murdering Mr Litvinenko.
When Russia refused to extradite Mr Lugovoi, Britain expelled four Russian diplomats and Moscow followed suit. Russian officials have described the action against the British Council as a retaliatory measure.
On Wednesday, a British Council spokesman said Russian staff in St Petersburg and Yekaterinburg were "summoned for interview by the FSB at their headquarters and subsequently visited in their homes late last night by officials of the Russian Ministry of the Interior".
They have been called to more interviews on Wednesday, he said.
"Our main concern is the safety and security of both our Russian and UK staff and we are deeply concerned by both these incidents," he added.
Conservative former foreign secretary Sir Malcolm Rifkind told the BBC the episode had "absolutely nothing" to do with the British Council and was rooted in "the very strong reaction of President Putin" to British attempts to extradite the man suspected of murdering Mr Litvinenko.