A spokesman for the Kremlin said Thursday that Donald Trump's foreign policy approach is "phenomenally close" to that of Russian President Vladimir Putin.

"They [Putin and Trump] set out the same main foreign policy principles and that is incredible," Dmitry Peskov, the Kremlin spokesman, said in New York on Thursday, Reuters reported.

Peskov, who was visiting the United States for a chess tournament, made the comments two days after Donald Trump was declared the president-elect of the United States.

"It is phenomenal how close they are to one another when it comes to their conceptual approach to foreign policy," Peskov continued. "And that is probably a good basis for our moderate optimism that they will at least be able to start a dialogue to start to clear out the Augean stables in our bilateral relations."

The spokesman's remarks were carried by Russian-controlled television broadcaster Channel One.

Relations between the United States and Russia have deteriorated in recent years, due to Moscow's intervention in Ukraine and the ongoing conflict in Syria. Trump has indicated that he would be open to cultivating warmer ties to Russia, including by cooperating with Moscow in Syria.

Peskov noted, however, that it would take time to repair relations between the United States and Moscow.

"An atmosphere of mutual trust takes years to achieve," he said. "It's not possible to just declare that there is an atmosphere of mutual trust, especially after such serious damage was done in the last few years to our relations."

Trump has been scrutinized by making friendly statements about Putin, though the business mogul-turned-politician maintains that he has no relationship with the Russian president. Putin has returned the compliments by making positive statements about Trump.

Separately, Russia's deputy foreign minister told the Interfax news agency on Thursday that the Russian government was in touch with members of Trump's political team during the presidential election campaign.

Trump met with President Obama on Thursday morning at the White House, beginning a transition that will see the businessman enter the White House in January.