President Donald Trump said Elon Musk has "lost his mind" as the pair's feud made waves in Moscow with Russian officials opening the door to the SpaceX billionaire.

The pair's tirades came to a head last night when Musk called for Trump to be impeached, with former Republican advisor Steve Bannon suggesting the X owner should be deported.

When asked about reports of a scheduled call with Musk later today, President Trump told ABC News: "You mean the man who has lost his mind?"

Now, the story has reached as far as Moscow, with senior officials weighing in on the spat.

President Donald Trump and Elon Musk have had a very public fallout

Senior security official and former President Dmitry Medvedev said: "We are ready to facilitate the conclusion of a peace deal between D and E for a reasonable fee and to accept Starlink shares as payment. Don't fight, guys!"

Nationalist senator Dmitry Rogozin added: "Elon, don't be upset!

"If you encounter insurmountable problems in the US, come to us. Here you will find reliable comrades and complete freedom of technical creativity."

Kremlin spokesman Dmitry Peskov, when asked about the clash, said it was an internal matter for the US, adding: "Presidents handle a huge number of different things at the same time, some more and some less important."

Deputy head of Russia's Security Council Dmitry Medvedev opened the door for Musk

Kremlin spokesman Dmitry Peskov seemed to suggest Trump would come out on top

An online poll suggests that while the majority of Americans back neither in the dispute, Americans are more likley to side with President Trump over Musk.

The YouGov poll had 28 per cent of Americans picking President Trump, eight per cent backing Musk, and 52 per cent siding with neither.

With Democrats, amongst those who picked a side, 11 per cent supported Musk against four per cent for President Trump.

Meanwhile, the President is vastly more popular with Republicans, with 71 per cent backing Trump, compared to just six per cent for Musk and 12 per cent for neither.

A Tesla vehicle is parked on West Executive Avenue near the White House

Following the extraordinary spat between the two men, shares in Musk's Tesla closed down 14 per cent, losing about $150 billion in market value in the largest single-day decline in value in the electric vehicle maker's history.

In pre-market trading today, they pared some of those losses, rising as much as five per cent after the early news that the two men were scheduled to speak.

According to a senior White House official, Trump is reportedly considering selling or giving away the red Tesla car he purchased earlier this year.