NEW YORK -- Vladimir Putin’s spokesman said Thursday the Russian president is really hoping for improved relations with the United States when Donald Trump becomes president, describing the two men as “very much alike” in how they see the world.

Russia hopes “for their good personal relationship,” Dmitry Peskov said in an interview with The Associated Press.

Peskov cautioned, however, that it will take time to restore trust in relations that are at their lowest point in decades.

Suspicions about Trump’s relationship with Putin’s government dogged his presidential campaign, in large part because the United States accused Russia of hacking into Democratic Party email systems in an apparent effort to influence the outcome of the election.

Peskov said Russian experts were in contact with some members of Trump’s staff during the campaign, but he reiterated that the Russian government and security agencies had nothing to do with the cyberattacks. A Trump spokeswoman denied there were any contacts between the campaign and “any foreign entity.”

Once Trump is sworn in on Jan. 20, Peskov said Putin will be looking forward to conversations with the new U.S. leader.

Get Breaking News Delivered to Your Inbox

“He has been a very firm supporter of the idea of good relationship between our countries, because we do carry a joint responsibility for strategic stability in the world, strategic security,” Peskov said, speaking in near-fluent English. He said Russia and the U.S. must address the “very, very dangerous challenge of global terrorism” together.

Trump has praised Putin as a strong leader and said he wants to be friends with Russia and join forces in the fight against terrorism, but he has outlined few specifics of how he would go about improving relations.

CBS News correspondent Elizabeth Palmer reports Russia’s enthusiasm for Trump’s win was on show at watch parties all over Moscow on Wednesday.

“This is the victory that American people brought the whole world,” a man at one party told CBS News.

Peskov said the two leaders are “very much alike ... in their basic approaches toward international affairs.” He noted that Putin and Trump had used almost the same language in recent weeks to stress that their country came first but they were ready to have good relations with the rest of the world.

This is a good reason “to believe that they will manage to establish good relations,” Peskov said. “We shouldn’t expect them to agree on everything. ... Unfortunately, we do have a very, very loaded luggage of disagreements now.”

“But if we are wise enough to start speaking to each other, and try to listen to each other’s concerns, this will be a real success,” he stressed.

Peskov is close to Putin, almost always by his side on foreign trips and at meetings with foreign leaders. It is highly unusual for him to travel abroad separately, but he is chairman of the board of the Russian Chess Federation and came to New York to attend Friday’s opening of the world championship match between Russia’s Sergei Karyakin and Norway’s Magnus Carlsen. The organizers have invited Trump to attend, but it was unclear whether he would accept the invitation.

Peskov said the U.S.-Russia relationship is “a victim” in every U.S. election, but this year was “quite unprecedented.” He said the Kremlin was “very surprised” when Putin became part of the campaign and when Trump was described as unpatriotic and unfit to be president for saying he was ready to speak to the Russian leader. “It’s so illogical,” Peskov said.

In addition to denying any Russian role in the hacking, he protested what he said were “hostile” threats from Washington of counter-measures against Moscow, including from Vice President Joe Biden.

Peskov said five top Russian banks were subjected to a heavy cyberattack Wednesday that their security systems managed to repel. He said Russia could blame Biden for saying Russia would have to pay the price, but if the two countries blame each other for everything “it will not help the situation.”

“We are all living in a very, very dangerous world and the only possibility for all of us to improve this world is to start to speak to each other and to start to cooperate,” he said. “And we do hope, and President Putin really hopes, that we’ll have an opportunity for optimism ... in our relationship with the United States.”