Putin stressed the importance of the two nations engaging in constructive dialogue in order to enhance global stability and to tackle global challenges and threats, according to a Kremlin news release.
"This would allow us to make progress in promoting pragmatic cooperation designed for the long term," the Russian President said.
Putin also noted that the principles of equality and mutual respect were the basis of developing relations between the two countries.
Last year, observers noted that Putin addressed then-President-elect Trump
, rather than President Barack Obama, in his annual greetings statement to foreign heads of state and government, saying he hoped for a "whole new level" in the two countries' interaction.
In this year's message to Syrian President Bashar al-Assad, Putin said Russia would continue to assist Syria "in upholding its state sovereignty, unity and territorial integrity, and promoting a political settlement and economic recovery."
The Russian leader also expressed hope that the situation in Syria would "change for the better" in 2018.
"Defeating terrorists and rapidly bringing the situation in the Syrian Arab Republic back to normal would be in the best interests of the whole world and would improve security in the Middle East," he said.
In his greetings to Turkish President Recep Tayyip Erdogan, Putin highlighted an improvement in bilateral relations and "substantial" progress in Russia-Turkey cooperation in the past year.
"By working closely together our countries have succeeded in preventing the terrorist threat from spreading further across the Middle East and created conditions for launching the political settlement of the Syrian conflict," his message reads.
Putin's greetings to Britain's Queen Elizabeth II and Prime Minister Theresa May "pointed out that closer Russian-UK cooperation would be in the basic interests of the Russian and British people and Europe as a whole," according to the Kremlin.
His message to China for the New Year and its upcoming Spring Festival notes "more success in Russian-Chinese relations, with substantial growth in mutual trade and dynamic exchanges in science and technology, and culture and the humanitarian sphere" over the past year.
Putin also welcomes progress in Russia's relations with Japan and South Korea in greetings to their respective leaders.