The three lawmakers, from the opposition Labour Party, Scottish National Party and Green Party, are the first sitting members of parliament to take the government to the ECHR on the grounds of national security.
They say that the government's failure to hold an independent inquiry into the findings of a report into alleged Russian electoral interference breaches the right to free and fair elections.
They have taken their claim to the ECHR after London's High Court rejected the challenge in 2021.
On Thursday, the ECHR gave the British government until April 26 to respond to the allegations. The ECHR said that the request for responses did not mean the case had been found admissible.
Britain's Intelligence and Security Committee in 2020 published a report on Russia's threat to Britain, saying it could not make an assessment over whether Russian meddled in the 2016 referendum on leaving the European Union.
It said that Britain's intelligence services should investigate and make its findings public. It added it found credible evidence Russia had tried to influence a 2014 Scottish independence referendum.
Former Prime Minister Theresa May said she took allegations of Russian interference in elections seriously, though her successor Boris Johnson was accused of delaying the release of the report.
"I would point out this claim has been roundly rejected by UK courts," a spokesperson for current Prime Minister Rishi Sunak told reporters when asked about the case.
"More broadly, safeguarding our democracy will always be an absolute priority, and the UK has robust systems in place to protect our elections from interference."
(Reporting by Alistair Smout; additional reporting by Michael Holden)
