Moscow (CNN) Russian President Vladimir Putin is often at odds with US policy, but his annual press conference on Thursday highlighted an exception: He agrees with President Donald Trump's plan for a military exit from Syria.

Putin's regular year-end press conference is a chance to show off his mastery of the minutiae of domestic and international politics. And he used the occasion Thursday to weigh in on a story that is roiling Washington and its allies: Trump's surprise announcement of a US troop withdrawal from Syria.

The Kremlin leader's assessment? He agreed with Trump's opinion that ISIS had largely been defeated in Syria, and said it was time for the United States to go.

"As for defeating ISIS, I do generally agree with the President of the United States. We have struck major blows and advances. There are now concerns that those terror groups can infiltrate neighboring countries ... and pose a risk to Russia, the US, Europe and Central Asia," said Putin.

On Wednesday, Trump ordered staff to execute the "full" and "rapid" withdrawal of US military forces from Syria, declaring that the US has defeated ISIS.

"If the decision to withdraw was made, then it is a correct one," Putin said, adding that the United Nations had not legitimized the presence of US forces in Syria.

However, he also expressed skepticism about whether the US would in fact quit Syria.

"As far as the withdrawal of US troops is concerned, I really don't understand what it's about, because the US has been present for some 17 years in Afghanistan," he said. "They're (the US) still talking about withdrawing them, but they haven't done it yet."

Will Trump, Putin meet?

This isn't the first time Putin has paid Trump a compliment of sorts at his press conference. Recall that in 2015, well ahead of Trump winning the Republican nomination, Putin singled him out as a presidential front-runner, calling him "a bright and talented person without any doubt."

Things have been a bit more complicated since Trump took office, however. The US President canceled a planned meeting between the two leaders last month on the sidelines of the G20 meeting in Argentina. Putin also expressed his willingness to meet with Trump but said he was unsure whether it would come about.

"I don't know whether a meeting will happen," Putin said. "On multiple occasions I've said I am willing to meet, we have a number of issues to discuss, including our bilateral agenda."

Putin suggested that the pair's ability to talk would be constrained when the Democrats take control of the US House of Representatives in January, following midterm election gains.

"Of course, now power in the Congress is changing and I'm sure that there will be more attacks on the President. Whether or not he will be able to have direct dialogue with Russia as a result of that, I don't know," he said.

Putin added that he was concerned by the erosion of the democratic process in the West, including the US. "Trump has won the election but not everyone is willing to accept this victory despite that it is indisputable truth," he said.

Nuclear arms race fears

Putin also addressed concerns about the growing risks of a new nuclear arms race as he held his annual televised news conference in Moscow.

"The danger of the situation escalating is being downplayed," he said in response to a question about fears of nuclear war.

Putin expressed the hope that humankind would have enough common sense "not to go to extremes." He also warned that the lowering of thresholds relating to nuclear capability "could really lead us to catastrophe."

Russia has criticized the US over the Trump administration's plans to withdraw from the Intermediate-Range Nuclear Forces Treaty, saying it risks the breakdown of international arms-control agreements.

This year's news conference is Putin's 14th, according to state-run media outlet RT.

The widely anticipated event, broadcast live on Russian TV, is a chance for hundreds of Russian and international journalists to pose questions on a range of subjects from the purely domestic to global affairs. Many hold up signs and banners as they seek to attract Putin's eye.

This year's marathon session wrapped after close to four hours, during which Putin appeared unruffled by the many issues raised, trotting out a raft of facts and figures -- and even making the odd humorous remark.

Journalists at Russian President Vladimir Putin's annual end-of-year news conference hold up signs to attract his attention.

Ukraine tensions

Questioned about Russia's detention of Ukrainian sailors in the Kerch Strait off Crimea last month, Putin laid the blame for increased military tensions at the door of the Ukrainian government.

The Ukrainian servicemen's action was a provocation designed to boost domestic support for President Petro Poroshenko ahead of elections in the country next year, he said.

Putin also pointed the finger at Kiev for the suffering of ordinary citizens in Ukraine's eastern Donbas region.

"Who do you think imposed the economic blockade on Donbas? The Ukrainian government," he said. "They are shooting at their citizens which they believe are Ukrainian citizens. Every day peaceful men and women are dying."

Russia and Ukraine have been locked in long-simmering conflict since the annexation of Crimea by Russia in 2014, and a war between Ukraine and Russian-backed separatists in the country's east has claimed more than 10,000 lives.

Putin Thursday disputed that Crimea had been annexed, since residents voted in a referendum to leave Ukraine, and argued that sanctions imposed by Western nations against Russia were effectively penalizing the people of Crimea.

Most of the world condemned the 2014 referendum in Crimea -- held after unidentified armed men had taken control of its administrative buildings and key military sites -- as illegitimate.

'Russophobic' mentality over Skripal case

Putin declined to comment on the poisoning of former Russian double agent Sergei Skripal and his daughter Yulia in the English city of Salisbury earlier this year.

But he drew a contrast between the world's reaction to that case and the killing of Saudi journalist Jamal Khashoggi in the Saudi consulate in Istanbul in October.

While "a whole heap of sanctions has been imposed on Russia" in connection with the Skripals, there has been "silence" over the Khashoggi case with regard to Saudi Arabia, he said.

That is very clearly down to a "Russophobic" mentality aimed at containing Russia's development to benefit its competitors, said Putin.

The UK government has accused Moscow of being behind the nerve agent attack on the Skripals , a claim Russia has consistently denied.

Putin described the Russia-UK relationship as "gridlocked" and suggested that could have an effect on the global economy, adding that Russia was interested in restoring its relationship with Britain.

As for Brexit, it's a domestic affair and the UK government should follow the wishes of the people, Putin said. "I hope that common sense prevails," he said.

Putin returned to the subject of Brexit late in the news conference as he raised concerns over the democratic process in the West.

"There was a referendum but no one actually wants to acknowledge the results," he said.