Fifa has refused to reveal how many drugs tests it has conducted on Russia’s World Cup squad following their staggering start to the tournament.

The game’s governing body would also not disclose whether any had taken place beyond those post-match amid a call from one of sport’s most senior anti-doping officials for it to publish details of each one carried out at football’s flagship event.

That came from the chief executive of the United States Anti-Doping Agency, Travis Tygart, who also said Russia must be aggressively tested to safeguard public confidence in the integrity of the World Cup.

Even before a ball was kicked at the tournament, Fifa was under pressure to ensure it did not witness a repeat of sport’s worst doping scandal - in which Russia covered up thousands of positive tests in and around the Sochi Winter Olympics - pressure the performance of its national team has only compounded.

Just days after being branded the worst side ever to stage the World Cup, Stanislav Cherchesov’s men produced the best start by a host nation - and one of the best by any country.

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Victories over Saudi Arabia and Egypt by an aggregate score of 8-1 propelled them into the knockout stage - and with a Group A game to spare - for the first time since the fall of the Soviet Union.

As of Thursday morning, data on the distances covered and speeds reached by individuals and teams at the World Cup showed Russia’s players had collectively run further than any other team in both matches.

Tygart, the man who brought down Lance Armstrong, told Telegraph Sport “international rules” stipulated sudden improvements in the sporting arena should always be investigated.

“Extraordinary performances demand additional tests,” he said.

Fifa, which has repeatedly described Russia as “one of the most tested teams prior to the 2018 Fifa World Cup”, refused to reveal whether such tests had taken place.

A spokesman said: “When it comes to tests during the competition, please understand we cannot comment.”

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Tygart last week warned it would be “naive” not to think Russia could violate anti-doping rules during the World Cup, a tournament he declared it should have been stripped of after being found to have orchestrated a systematic doping programme that sabotaged the London and Sochi Olympics.

An investigation also implicated Russia’s entire squad at the 2014 World Cup - some of whom are still playing for their country - prompting a Fifa inquiry.

The governing body last month announced the partial closure of that investigation, ruling there had been “insufficient evidence” to charge members of the current squad with an anti-doping rule violation, although it said inquiries into those not picked for this tournament were “ongoing”.

Tygart said that when it came to testing Russia players at the World Cup, Fifa had to “go beyond the basics to give confidence to the public that they’re doing it the right way”. But he also warned against using the team’s performances to impugn guilt without hard evidence.

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Indeed, there are lots of possible reasons why they are running so far and fast. Among them are the fact they are at home and the adrenalin will be flowing perhaps more than it would otherwise; the least the country will expect is for the players to give their all; and they may be trying to compensate for their perceived technical inferiority.

Tygart said: “It’s really unfair to draw conclusions about individuals or teams based solely on performances.

“I think athletes deserve to have a system in place that protects them and corroborates when they say - when the questions will inevitably come - ‘I have a gold-standard programme in my country and that gives me proof that I’m being held to the highest standards, so you cannot only hear me say I’m clean but you can also trust that I’m clean’.

“And, unfortunately, there are countries - and obviously Russia, where it’s been exposed - where that’s not the case.

“And shame on the leaders of sport and the leaders of that country for not giving these World Cup players the opportunity to say when these questions are coming at them now - which obviously they are - ‘Look, we’re held to the highest standards and we’ve been held to the highest standards’.

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“We know that’s not the case, right? We know what’s happened in just the recent past.”

Tygart said it was unclear how much Russia - still banned from world athletics and Paralympic sport for refusing to admit to its state-sponsored programme - had cleaned up its act.

“You look at its testing statistics, they’re not where they should be,” he said. “We don’t see any individual names of people tested.

“Whatever happens at the games is one thing. The key part is what were they doing over the last six-to-12 months?”

He added: “It’s unfortunate the questions are being asked and it’s really unfair to the players themselves - and I hate that this is happening.

“Obviously, it’s happening because of the failure of the leaders of that country’s sport. That’s not the players’ fault.”