Foreign Secretary William Hague said the Government will "make representations to the Russian authorities as necessary" after 30 Greenpeace activists and journalists, including six Britons, were charged with piracy following an Arctic oil rig protest.
Mr Hague raised the case with his Russian counterpart Sergey Lavrov last week and the UK's ambassador in Moscow discussed the issue with deputy foreign minister Sergei Ryabkov yesterday.
The Foreign Secretary said consular officials had met the British nationals who had been arrested and remained in regular contact with them to ensure their welfare.
British freelance videographer Kieron Bryan and UK activists Philip Ball, Alexandra Harris, Anthony Perrett, Frank Hewetson and Iain Rogers have been charged over the protest at Russian state oil company Gazprom's platform in the Arctic's Pechora Sea.
A group of 28 activists and two journalists were detained when armed Russian officials boarded the Greenpeace vessel the Arctic Sunrise close to the oil rig and brought the ship and crew to the Port of Murmansk, where they are being held.
All have now been charged with piracy by Russian state prosecutors - charges which come after the country's president Vladimir Putin said it was clear the activists were not pirates.
Mr Hague discussed the situation with Greenpeace UK's executive director John Sauven and said the Government would raise concerns the environmental campaign group had about due process or welfare with the Russian authorities.
The Foreign Secretary said: "We would remain in close contact with all other nations whose citizens were involved, and make representations to the Russian authorities as necessary."
Mr Sauven said the decision to bring charges of piracy against the activists and freelance journalists was "completely outrageous".
He said: "There isn't a shred of evidence to justify holding these activists, let alone charging them with piracy.
"Greenpeace, and the thousands of people who support us, will not stand idly by while these peaceful protesters are locked up on these absurd charges.
"This Saturday a mass protest will be held outside the Russian embassy in London and the consulate in Edinburgh.
"The Russian authorities should be in no doubt that for as long as they imprison our activists and independent freelance journalists, Greenpeace will campaign to have each and every one released."
Earlier the parents of Mr Bryan said it was "ludicrous" he had been charged with piracy.
Speaking to BBC Breakfast, Andy and Ann Bryan said they were "absolutely stunned" their 29-year-old son had been charged and hoped senior government ministers would intervene.
Mr Bryan said: "He's not a Greenpeace activist, he's not an activist, he's not a member of Greenpeace. He's simply employed by them to make a film, just like any other assignment he might have taken as a freelance."
Mrs Bryan said: "He was doing his job, earning his living.
"It's a ludicrous charge, absolutely ludicrous. How can two people, armed only with a banner and a piece of rope to climb up an oil rig, seize an oil rig?"
The couple, from Shebbear in Devon, said they had not been able to speak to their son for more than a week.
Mr Bryan's MP, Labour's deputy leader Harriet Harman, has written to Mr Hague to ask him to intervene, his father said.
Mr Bryan, a film-maker and videographer, previously worked at The Times. He was hired on a short-term contract by Greenpeace to document its work on Russian oil exploration in the Arctic Circle.
Greenpeace is campaigning against attempts by companies to extract oil from the waters of the Arctic Ocean, warning that a spill would be highly environmentally damaging, and extraction of more fossil fuels will add to climate change.
Gazprom's plans to start drilling from the Prirazlomnaya platform in the first quarter of 2014 raised the risk of an oil spill in an area that contains three nature reserves protected by Russian law, campaigners said.
Mr Bryan said his son understood there was an "element of risk" in taking the job but he "couldn't have imagined" the reaction from Russian authorities.
"Given what Putin said last week about the fact that they clearly weren't pirates, the announcement that they were being charged with piracy absolutely stunned us," he said.
"He understood that there was an element of risk and the Russian authorities would be aware of what they were doing, but certainly he couldn't have imagined ... that this would have been their reaction.
"Obviously now the Government are involved and hopefully they will take it forward and make representation. That's what we want really because he clearly should not be there having been charged with that offence."
Greenpeace International executive director Kumi Naidoo said: "Our activists have been charged with a crime that did not happen, they are accused of an imaginary offence.
"There can be no doubt about why the charge of piracy has been brought and the legal hammer wielded.
"An effort is under way to intimidate us, but our peaceful passionate campaign against Gazprom and all other Arctic drillers will not be silenced.
"A profound injustice is right now being perpetrated against our friends, our brothers and sisters, our sons and daughters who sit in jail.
"I call on people across the world to stand with us against Gazprom and all oil companies who want to drill in the Arctic, join us in this fight against bullies of the very worst kind."
Mr Sauven said one of the British activists was taken ill before hearing his charges.
"As a precaution, he was taken to hospital for examination, but was not required to undergo treatment. Contrary to inaccurate reports, he did not have a heart problem.
"We remain in close contact with the activists and expect the Russian authorities to provide any appropriate care where needed."
The family of the activist, whom Greenpeace UK is not naming, were aware of the situation, he added.
"It is standard procedure for each crew and passenger on a Greenpeace International ship to have undergone a full medical check-up before boarding."
Following the meeting with the Foreign Secretary Mr Sauven said: " We specifically discussed what intervention he could make on behalf of the six detainees to improve the conditions they are being kept in and enable them to make direct contact with their families.
"The Foreign Secretary assured me that he would discuss these matters with the Russian authorities.
"We also explored how Greenpeace and the Foreign and Commonwealth Office could work together to facilitate the release on bail of those being held and we will have further conversations with officials in the coming days.
"I thanked the Secretary of State for all the assistance the consulate staff had given to the six detainees in Murmansk."