United States President-elect Donald Trump has shared a "very nice" letter from Russian President Vladimir Putin, sending his "warmest Christmas and New Year greetings".

Key points: Letter voiced hope of improving bilateral ties between US and Russia

Letter voiced hope of improving bilateral ties between US and Russia Mr Trump said Mr Putin's thoughts are "so correct"

Mr Trump said Mr Putin's thoughts are "so correct" Letter comes after comments from both leaders about the need to strengthen their countries' nuclear arsenals

Mr Putin's letter, dated December 15, said serious global and regional challenges "show that the relations between Russia and the US remain an important factor in ensuring stability and security in the modern world".

"I hope that after you assume the position of the President of the United States of America we will be able — by acting in a constructive and pragmatic manner — to take real steps to restore the framework of bilateral cooperation in different areas as well as bring our level of collaboration on the international scene to a qualitatively new level," Mr Putin wrote.

He finished it on a lighter note, wishing Mr Trump and his family "sound health, happiness, wellbeing, success and all the best".

In response, Mr Trump said: "His thoughts are so correct."

"I hope both sides are able to live up to these thoughts, and we do not have to travel an alternate path."

Mr Putin's spokesman Dmitry Peskov confirmed the President sent the letter, "voicing hope for an improvement of bilateral ties", according to the Interfax news agency.

Mr Trump's transition team described the text as an unofficial translation.

The exchange comes after comments by Mr Trump and Mr Putin alike about the need to strengthen their countries' nuclear arsenals.

Mr Trump reopened the debate over nuclear proliferation on Thursday, declaring on Twitter the US should "greatly strengthen and expand its nuclear capability" until the rest of the world "comes to its senses" regarding nuclear weapons.

Those comments echoed an earlier statement by Mr Putin, who had said strengthening his country's nuclear capabilities should be a chief military objective in the coming year.

But Mr Putin downplayed the significance of Mr Trump's comments at a marathon end-of-year news conference, saying he sees "nothing special" in Mr Trump's pledge to strengthen the US nuclear forces and that the statement is in line with the President-elect's campaign promises.

ABC/AP