MOSCOW, Russia  - President Barack Obama's national security advisor on Monday handed a "constructive" message from the US leader to Russian President Vladimir Putin, days after the former foes exchanged Cold War-style blacklists in a row over human rights.

The Kremlin praised the note, personally handed over in Moscow by White House National Security Advisor Tom Donilon to Putin, as containing new ideas and said it included proposals about nuclear arsenals.

Donilon, the highest-ranking American to visit Russia since Obama's inauguration for a second term in January, walked into a vicious diplomatic storm in Moscow that whipped up over the weekend. The United States on Friday published a list of 18 Russians it was blacklisting over human rights abuses. Russia a day later angrily responded with a similar list of its own in a tit-for-tat move.

But Putin joined Donilon's talks with his Russian counterpart Nikolai Patrushev at the Kremlin, a move that the Kremlin had kept under wraps until the last moment in a apparent bid to remind Washington of its displeasure. The Kremlin confirmed Donilon handed over Obama's message, which Putin's foreign policy advisor Yuri Ushakov said contained proposals on nuclear weapons arsenals, missile defence and improving bilateral trade. "The message is written in a very constructive tone," he said, quoted by the Interfax news agency.

"Some ideas have already been talked about but there are some new elements which our country will study in the most attentive way and give a corresponding response," he added, without specifying further on the contents of the message.

Ushakov said the events of the past days showed that while the Obama administration "wants to actively develop relations in many areas", the United States "still has some Russophobes who want to throw a spanner in the works."

Donilon held a morning meeting with Foreign Minister Sergei Lavrov who said that the American side had emphasised they did not want the "irritations" to spoil the strategic nature of US-Russia relations.

The US lists 16 Russians allegedly linked to the death of jailed lawyer Sergei Magntisky in 2009 as well as two Chechens who stand accused of murder. They are barred from travelling to the US or holding assets there.

Russia slammed the move as unfriendly and a day later hit back with its own blacklist of 18 Americans, including several well-known figures linked to detention practices at the Guantanamo Bay prison.

"The first person to feel the effects of Washington's blacklists is going to be T. Donilon. He is not coming to us at the best of times," the head of the Russian lower house of parliament's foreign affairs committee Alexei Pushkov wrote on Twitter.

Even before the blacklist row, the visit was seen as having huge importance as Obama looks for new bilateral nuclear weapons cuts and support from Russia in the North Korea crisis.

The US blacklist stems from the Magnitsky Act which Washington passed last year, infuriating Russia. Moscow responded by banning adoptions of Russian children by Americans, a move that caused an international outcry.

The death of Magnitsky in pre-trial detention in 2009 at the age of 37 - after being accused of a fraud scam that he claimed to have uncovered - has come to symbolise the Kremlin's failure to protect human rights.

Meanwhile, Uzbekistan President Islam Karimov on Monday warned Russian President Vladimir Putin over the growing dangers of extremism in Central Asia, his first trip abroad since claims from the exiled opposition sparked rumours about the Uzbek strongman's health.

The talks marked a rare visit to the Kremlin for Uzbekistan's first and only post-Soviet leader, whose country has fallen into increasing isolation, not only with strained relations with the West but also testy ties with former Soviet master Moscow.

Karimov, who has sought to distance Uzbekistan from both its Soviet past and Western culture, last visited Moscow for a bilateral visit back in April 2010, although he attended a regional summit in the Russian capital in May 2012.

Russian state television pictures showed Karimov in apparent good form and in characteristic style warning Putin about the danger of extremism in the volatile ex-Soviet Central Asia region bordering Afghanistan.

"No-one has declared war on us. But the consequences of the expansion in terrorism, extremism and religious radicalism could be far worse than open war," said Karimov.

He warned that the risks were particularly real ahead of the planned withdrawal of coalition troops from Afghanistan, with which Uzbekistan shares a short but vulnerable border.

"The balance of powers in the region is constantly changing and not always for the best. We need to meet more often," Karimov told Putin, noting Russia's key role in the region.

Putin said that both Moscow and Tashkent agreed on the need to help the Afghan leadership "in stabilising the situation and fighting against narcotics, terrorism and extremism."

He hailed Karimov's visit, saying "the positions of our countries are either the same or very similar," and vowed to bolster trade with the country of 30 million people.

Karimov's vigorously secular regime has over the last years led an unrelenting campaign against radicalism in the overwhelmingly Muslim country, the most populous in Central Asia.

Although Karimov has always admired Putin, he has been infuriated by the presence of Russian military bases in Tajikistan and Kyrgyzstan, and its support for the Kyrgyz government's hydro-electic projects.

But a major focus of the visit is on Karimov himself after he appeared to briefly disappear from public life in March in what the exiled opposition said was an enforced absence due to a heart attack.

His daughter Gulnara has rubbished the allegations on her widely-followed Twitter feed, pointing to a video that showed Karimov dancing at the Turkic New Year (Navruz) celebrations on March 19.

But exiled opposition figure Muhammad Solih told the Uzbek Service of Radio Free Europe that he had heard from inside the country that Karimov had suffered a heart attack after Navruz.

However Uzbek television at the end of March showed pictures of an apparently healthy Karimov, 75, meeting the Kazakh foreign minister.

The trip to Moscow was Karimov's first foreign visit this year after he attended a regional summit in Turkmenistan in December.

The flurry of rumours about his health highlighted the internal political jockeying in Uzbekistan with figures including Gulnara herself and long-serving Deputy Prime Minister Rustam Azimov seen by Western commentators as possible future leaders.

Gulnara, also known as a fashion designer, pop star and a diplomat, in late March blasted Azimov on Twitter in the first instance where she has so overtly flexed her political muscle at home.