Mr Wallace made the comments a week on from police identifying two men, using the names Alexander Petrov and Ruslan Boshirov, as suspects in the attempted murder of former Russian spy Sergei Skripal and his daughter Yulia.
The pair, who are said to be operatives of the country’s GRU military intelligence service, entered the UK from Russia via Gatwick Airport in March, smuggling the nerve agent by using a perfume bottle.
Authorities believe the men smeared the highly toxic chemical on a door handle at the Wiltshire home of Mr Skripal, leaving he and his daughter Yulia critically ill.
Mr Wallace, leading a Government debate on the Salisbury poisonings in the Commons today, said: “When a hostile state is determined to try and use its full resources to penetrate another state, the challenge is much greater.
“The logistical support of that state in assisting its agents is significant and that means for example that these two individuals travelled on a genuine Russian passport, making it harder to spot, that there was clearly some form of attempt to create a legend to make sure that they circumvented obviously our checks and, only in a speculative way, but no doubt at the other end of that aeroplane journey there was some, I should think the baggage checks weren’t probably as good as they might be.”
The allegations are staunchly denied by the Kremlin.
Mr Putin today said the men had been discounted as members of his shadowy security network.
The Russian president’s intervention risks widening the gulf between Russia and the UK over the attempted assassination, which triggered a wave of diplomatic expulsions by both sides.
Mr Wallace was asked in the Commons whether the Government would consider further expulsions, to which he said: “We will keep all options on the table.
“For now we are working on a number of measures to push back Russia’s activities and do our best to degrade their intelligence services.”
Mr Wallace later said requests for Russia to account for what happened in Salisbury had been met with “obfuscation and lies”, saying their response merely “reinforces their guilt”.
And he called on Mr Putin to hand over the suspects for a trial, saying: “I believe in the British justice system and if they are innocent they will be acquitted, so yes I have every faith and so I would urge him to hand those individuals over for a trial.
“They are suspects and they are innocent until proven guilty.”