Stan and Caroline Sturgess believe British authorities are withholding details of the incident.
Investigative website Bellingcat traced extensive travel by Sergeev around Europe, Central Asia and the Middle East before the Skripal attack.
Russia has repeatedly denied any involvement in the poisoning, as have the two men identified by Britain.
The Kremlin responded after Prime Minister Theresa May's spokesman said the interview contained lies and blatant fabrications and called it an insult to the public's intelligence.
Alexander Petrov and Ruslan Boshirov denied being members of Russian military intelligence, telling the Kremlin-backed RT news network they were in the English city purely as tourists.
British authorities have issued European arrest warrants for Alexander Petrov and Ruslan Boshirov, two suspected members of Russian military intelligence, the GRU. a
Russia has long denied any involvement in the attack on Sergei Skripal and his daughter Yulia in Salisbury and insisted it is ready to cooperate on any investigation.
The sanctions taking effect this month will limit exports to Russia of US goods and technology considered sensitive on national security grounds.
Former Russian double agent Sergei Skripal and his daughter Yulia were poisoned in Salisbury with the Soviet-made Novichok nerve agent - they spent weeks recovering in hospital.
The Kremlin said on Monday it was sorry to hear that a British woman, Dawn Sturgess, had died after being poisoned by a nerve agent, but said any suggestion that Russia was involved would be "quite absurd."
Amesbury lies seven miles (11 kms) to the north of Salisbury, where in March Russian former spy Sergei Skripal and his daughter Yulia, fell severely ill after being poisoned by nerve agent.
Relations between London and Moscow have plumbed new lows in recent weeks following the poisoning of former double agent Sergei Skripal and his daughter Yulia on March 4.
Mempunyai pengalaman serupa di tanah air, kita mengutuk sekeras-kerasnya penggunaan senjata kimia dalam keadaan apa sekalipun, katanya.
Sergei Skripal is in a critical condition after suspected exposure to what police have called "an unknown substance".