MOSCOW -- A top Russian diplomat and Vladimir Putin’s spokesman said Thursday that Russian experts were in contact with some members of President-elect Donald Trump’s staff during the presidential campaign, a period in which the United States accused Russia of hacking into Democratic Party email systems.

A spokeswoman for Trump denied the assertion, but it raised the ongoing suspicions about the president-elect’s relationship with Putin’s government that had dogged his campaign with former Secretary of State Hillary Clinton.

Russia is hopeful that a Trump presidency will herald improved relations with the United States. But, in a sign of the cold realism that Putin is known for, Moscow is not betting on an immediate drastic turnaround in the strained relationship.

And while Trump himself has said he wants to be friends with Russia and join forces in the fight against terrorism, he has outlined few specifics as to how he would go about it. President Obama began his presidency with a similar goal, only to see progress unravel over the conflicts in Ukraine and Syria.

Putin spokesman Dmitry Peskov told The Associated Press in an interview in New York that Russian experts had contacts with people in both the Trump and Clinton campaigns. He said such contacts are “quite natural, quite normal.”

“And our experts, our specialists on the U.S., on international affairs ... Of course they are constantly speaking to their counterparts here, including those from Mr. Trump’s group,” Peskov said.

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“Of course, it’s quite natural that Russian experts are trying to maintain the dialogue with people from different camps. It’s very important to understand the main streams, and understand the main tendencies, nuances in the positions of different parties, different camps here in the United States,” he said.

Earlier, Deputy Foreign Minister Sergei Ryabkov was quoted as telling the Interfax news agency that “there were contacts” with influential people in Trump’s circle. “I don’t say that all of them, but a whole array of them supported contacts with Russian representatives.”

Trump spokeswoman Hope Hicks denied such contacts.

“It never happened,” she said. “There was no communication between the campaign and any foreign entity during the campaign.”

Among Trump’s inner circle was Paul Manafort, a longtime Republican operative who’d advised a pro-Russian Ukrainian political party before its ouster over alleged corruption. Manafort left the campaign after those contacts were made public.

The U.S. government believes Putin might have interfered in the presidential election. The intelligence community has concluded that Russia was responsible for hacking into the emails of the Democratic National Committee and Clinton campaign chairman John Podesta and gave them to WikiLeaks, which released them. Some embarrassed and damaged the Clinton campaign.

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.

In his comments, Ryabkov was careful not to overpromise.

“We do not feel any euphoria,” he said, recalling ups and downs in the Washington-Moscow relationship under both Republican and Democratic administrations.

“We wouldn’t like our public ... to have an impression that we are full of some rosy expectations. I have to say that the judgments about Russia aired by members of the Trump campaign and people from his entourage were quite tough. And we didn’t see any reason to revise our view that the election campaign in the U.S. in fact saw a bipartisan anti-Russian consensus.”

Still, speaking with the careful phrasing befitting the spy he once was, Putin has made it clear he expects a great deal from Trump. And, Trump has suggested he wants a far more transactional relationship with Putin than Mr. Obama has had.

Trump’s rise to the White House puts two men into seats of global power who are paradoxically both remarkably similar and wildly different.

Trump’s praise of the Russian president as a strong leader, his suggestion that the U.S. could abandon its NATO commitments and his vehement complaints about allegedly biased news media all appear to parallel Putin’s view of the world.

Trump has repeatedly called for better relations with Russia, frequently musing about a rosy world in which Russia and the U.S. get along. On Wednesday, Putin did the same, hoping that the “degraded” relations between the two countries would improve once Trump takes over. Putin noted, however, that the tension “is not our fault.”

Trump made no specific mention of Russia in his first post-election comments but made clear that he wants good relations with all nations “willing to get along with us.”

Putin would be pleased if the U.S. dropped the sanctions imposed for Russia’s annexation of Crimea and its involvement in the continuing war in eastern Ukraine. That could appeal to Trump’s sense that he is the master of the deal.

“I believe that Trump is a practical man; he will lift sanctions on Russia that are harmful to U.S. business,” Putin aide Sergei Glazyev told the state news agency Tass.

The U.S. sanctions have been a strong factor in Russia’s economic decline over the past two years, along with a plunge in prices for oil, its major export.