The export of arms to Russia has been banned since 2014 under sanctions imposed following the annexation of part of Ukraine.
Mr Ellwood told the House of Commons Arms Export Controls Committee that the guns were produced by Portsmouth-based company Accuracy International.
“Some of these weapons systems have now ended up in the hands of Russians that are now working in Eastern Europe,” he said.
“And these weapons are actually being aimed at British soldiers who are also based in support of the Baltic countries and on the NATO operations that are being conducted.”
He called for an investigation by the Department for International Trade, whose director general for trade relations Amanda Brooks was giving evidence to the committee.
Ms Brooks said the department was aware of reports of UK sniper weapons finding their way into Russian hands.
She assured Mr Ellwood: “There is an arms embargo in place for Russia, and therefore nothing has been licensed that would contravene that arms embargo.”
But she added: “We are aware that there were some sniper rifles that were licensed, if they were sporting rifles, either to individuals or dealers for sporting purposes only before that arms embargo was in place, which may be the source of those.”
DIT head of export control policy Chris Chew suggested that the weapons may come from a quantity of sniper rifles licensed for export to Russia in the late 1990s.
But Mr Ellwood rejected the explanations as “glib”.
“I don't believe these are 1990s weapon systems that are being used,” he said. “That would suggest that these weapons are 30 years old. I don't think that's the case here, and the evidence suggests that these are much more modern weapons systems.
“There is a difference between sports sniper rifles, and those designed for Arctic warfare, which is what this company sells. They're not designed to shoot animals, they're designed for military purposes.
“These aren't weapons from three decades ago. These are systems which have probably been sold elsewhere and ended up in the hands of people taking aim at British soldiers.”
He asked DIT to provide the committee with a full assessment as to how the weapons had fallen into Russian hands.
Andrew Smith of Campaign Against Arms Trade said: "The fact that Russian forces are using UK-made rifles is yet another sign of how broken the arms export system is. It is staggering that this was not already being investigated as a matter of priority.
“Weapons can easily change hands, and there is no such thing as arms control in a war zone. The lifespan of a weapon is often longer than the lifespan of the situation it is sold into.
“Once weapons have left these shores there is very little oversight of who is using them, and who they are being used against. The best way to stop weapons from being used in atrocities and abuses is not to sell them in the first place.”
There was no immediate response from Accuracy International to a request for a comment.
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