Moscow is being forced to readjust its expectations of a closer relationship with the US just four months after Donald Trump was elected President.

There had been celebrations in Russia at the thought of a White House that did not involve Hillary Clinton, with hopes it would end years of fractious diplomacy.

Donald Trump was given blanket coverage on state media and souvenir matryoshka dolls (at $AU45) and coffee mugs (slightly less at $10) imprinted with Mr Trump's face were snapped up by Russians and tourists.

But that heady excitement has now dissipated and the tone has changed in Russia.

Emotions running high

Andrey Kortunov, director of Moscow-based think tank the Russian International Affairs Council, said it was too early to make final judgements but there were "a lot of emotions, including anxiety" in Moscow.

"Right now many people are confused about what to expect from Donald Trump," he said.

Share Merchandise in support of US President Donald Trump has been hugely popular in Russia.

The chairman of the Foreign Affairs Committee in Russia's Upper House said there was a "paranoia" and "Russiophobia" brewing in the US.

Konstantin Kosachev made his comments after the resignation of Mr Trump's national security adviser Mike Flynn, who was forced out after it was revealed he'd spoken to Russian officials about sanctions, before the administration had been sworn in.

Share Konstantin Kosachev is the chair of the Foreign Affairs Committee in Russia's Upper House.

"I determined the reaction of the American establishment as paranoia, as Russophobia, as an attempt to set down red flags around Mr Trump and other members of his team in order to limit their ambition to start up some kind of dialogue with Russia," he said.

Foreign Minister Sergei Lavrov's spokeswoman Maria Zakharova said it was too early to suggest Moscow was disappointed at the turn of events.

"I mean the context between officials are just not started yet," she said.

"We're just looking forward to starting them."

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Usually glowing coverage toned down

The head of the Russia program at Chatham House in London, James Nixey, said it was clear Russians were not necessarily "jumping down the aisles" about Mr Trump's victory anymore.

"If he's unpredictable to you and me then he's of course unpredictable to the Kremlin as well," he said.

"The deeper thinkers in Russia do realise that Donald Trump could turn very sour.

"He's a sensitive man and doesn't take criticism very well. And when you have two strongmen and two super powers rubbing up against each other then a few tweets are not the basis for a relationship."

The usually glowing coverage of Mr Trump by Russia's state media has been toned down.

And the tabloid newspaper Komsomolskaya Pravda was derogatory of Mr Trump after his recent lengthy press conference.

Its headline declared: "As the saying goes, you need to be drunk to understand the true position of America's President".

Ms Zakharova would not say if the Trump administration's mixed messages were proving to be difficult to understand.

"What about the United States suggests it to be predictable or unpredictable?" she asked.

"Come on, be realistic."

"We were managing with Washington and latest years showed us and the world that Washington and the previous administration was absolutely unpredictable."

Share Donald Trump praised Mr Putin's leadership style during his campaign.

Waiting for clarity

Senate member Mr Kosachev told the ABC he was still optimistic.

"We definitely have some expectations left, we are optimistic that relations between the United States of America and Russia deserve better conditions," he said.

But Russia is still waiting for clarity on US foreign policy.

Share Papier mache caricatures depict a meeting between Mr Trump and Mr Putin.

The White House has said it wants a de-escalation of violence in eastern Ukraine and for Russia to give back Crimea.

That has been met with resolute defiance.

"N-E-V-E-R. Never. We already betrayed these people once," Ms Zakharova said.

What happens next will probably depend on the leaders' first meeting.

Presidents Putin and Trump will both attend the G20 summit in July.

Diplomats told the ABC it would be highly unlikely for Mr Trump to hold a bilateral meeting with Mr Putin before similar meetings with German and French presidents.

But there was speculation the US and Russian leaders would meet before July.

Mr Putin's spokesman Dmitry Peskov said there were no specific arrangements for an earlier meeting.