The resignation of Donald Trump’s national security adviser has reignited debate about the US administration’s alleged links with Russia after revelations Michael Flynn misled the Vice President about the extent of his contacts.

Mr Flynn admitted giving Mike Pence and others “incomplete information” about phone conversations with the Russian ambassador “because of the fast pace of events” during the transition period.

The Vice President initially said the national security adviser had not discussed sanctions implemented against Russia over the Ukrainian war and alleged interference in the US election with Sergei Kislyak, but Mr Flynn later conceded the issue may have come up.

Michael Flynn resigns as national security adviser over Russia row

Dmitry Peskov, a spokesperson for the Kremlin, confirmed the phone calls took place in December but denied he and Mr Kislyak had discussed easing sanctions.

Any assurances offered over the incoming administration’s new approach would breach diplomatic protocol and constitute a possible violation the Logan Act, which aims at keeping citizens from conducting diplomacy.

The Justice Department – under dismissed acting Attorney General Sally Yates - had reportedly warned the White House over the conversations last month, arguing that they could leave Mr Flynn vulnerable to blackmail.

His eventual departure on Monday evening came after the White House issued a statement saying Mr Trump was “evaluating the situation” over his adviser, who was previously dismissed by Barack Obama as head of the Defence Intelligence Agency in 2014.

The following year, Mr Flynn was paid to attend a gala dinner for state-owned broadcaster, and sat next to Vladimir Putin during the event.

Mr Flynn was one of several presidential appointments hailed by pro-Kremlin analyst Sergei Markov as a “fantastic team”, alongside Rex Tillerson.

Mr Tillerson, the Secretary of State, has had business ties in Russia for two decades as head of the Exxon Mobil oil and gas corporation and its join Russian venture Exxon Neftegas.

Vladimir Putin speaks with Rex Tillerson during the signing of a Rosneft-ExxonMobil strategic partnership agreement in Sochi in 2011. (AFP/Getty Images)

He has met the Russian President several times during the course of his business dealings, being bestowed with the Order of Friendship by Mr Putin in 2013, and was also linked with sanctioned Rosneft head Igor Sechin.

In an Exxon shareholder meeting in May 2014, Mr Tillerson said the anti-Russian sanctions putting millions of dollars in his firm at risk were not found to be “effective”.

He said he never lobbied against the sanctions during his confirmation hearing, where he was grilled on Russia’s record on human rights and intervention in Syria, telling Democrats that he would not “use the term [war criminal]” to describe Mr Putin.

When confronted by claims that Mr Putin was a “killer” in a Fox News interview, Mr Trump replied: “There are a lot of killers, we've got a lot of killers. What do you think? Our country's so innocent?”

The US President has reiterated his “respect” for his Russian counterpart, who complimented him during his presidential campaign.

Mr Trump also dismissed the FBI’s allegations that Russian hackers had interfered in his election, sparking a row with his own security agencies, and praised Mr Putin’s “very smart” decision not to immediately impose counter-sanctions in December.

He has denied having any financial links with Russia himself, tweeting last month: "Russia has never tried to use leverage over me. I have nothing to do with Russia - no deals, no loans, no nothing."

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A Trump hotel was proposed in Moscow in the 2000s but never built, while the President visited Moscow in 2013 to host the Miss Universe pageant.

Mr Trump's alleged activities during his stay were included in a dossier passed to the FBI, but could not be verified.

Shinzo Abe, the Prime Minister, said Mr Trump had “agreed” with Japan’s promotion of dialogue with Russia over territorial issues, as well as the Syrian and Ukrainian wars during his recent visit to the US.

The friendly overtures caused unease in Washington that has been worsened by Mr Flynn’s departure.

But Konstantin Kosachev, the chairman of the Russian State Duma’s foreign affairs committee, said the national security adviser’s removal represented “not just paranoia but something even worse.”

“Either Trump hasn't found the necessary independence and he's been driven into a corner...or Russophobia has infected the new administration from top to bottom,” he wrote in a Facebook post.

His counterpart in the lower chamber of the Russian parliament, senator Alexei Pushkov, tweeted shortly after the announcement that ”it was not Flynn who was targeted but relations with Russia”.