President Vladimir V. Putin of Russia in Berlin in October. He and President-elect Donald J. Trump spoke about Syria during a call on Monday. Credit Odd Andersen/Agence France-Presse — Getty Images

MOSCOW — President Vladimir V. Putin of Russia and President-elect Donald J. Trump spoke by telephone for the first time on Monday, agreeing to review what both consider the poor state of relations between the two countries, according to a statement from the Kremlin.

The two agreed “on the absolutely unsatisfactory state of bilateral relations,” said the statement, and they both endorsed the idea of undertaking joint efforts “to normalize relations and pursue constructive cooperation on the broadest possible range of issues.”

The issues discussed included trade and economic ties as well as combating terrorism. Mr. Putin was one of the first world leaders to congratulate Mr. Trump last Wednesday, sending him a telegram about an hour after he had emerged the victor, but the two men have not met nor had they spoken previously. Mr. Putin repeated the congratulations over the phone.

The Russian president said he hoped that Moscow could build a “collaborative dialogue” with Washington on the bases of “equality, mutual respect and noninterference in the other’s internal affairs,” the release said.

The two men also discussed Syria in the context of “the need to work together in the struggle against the No. 1 common enemy — international terrorism and extremism,” the statement said.

Although Mr. Putin maintained studied neutrality during the presidential race, the state-run news media, which answers to him, clearly pulled for Mr. Trump. Among other issues, Mr. Putin blames Hillary Clinton, then secretary of state, for the mass demonstrations that greeted his return to the presidency in 2012.

After Mrs. Clinton lost, the flagship state television news broadcast took to referring to her as the “blonde woman.”

During the campaign, senior United States security officials accused Russia of hacking the computers at the Democratic National Committee headquarters and releasing emails that proved embarrassing to the Clinton campaign. Mr. Putin denied any state role in the hacking.

The Russian government was one of the few around the world that was openly gleeful about the American election result, with members of the State Duma, the lower house of the Russian legislature, breaking into applause at the announcement. The United Russia party, loyal to Mr. Putin, dominates the Duma.

Mr. Trump and Mr. Putin developed something of a mutual admiration society during the election, particularly after Mr. Trump suggested that Crimea, which Moscow annexed from Ukraine, should belong to Russia and that the United States should ally itself with Russia and the Syrian government of President Bashar al-Assad to fight the Islamic State. Mr. Trump also suggested the United States might dilute its support for NATO, which Russia considers a main threat.

Much of the brief statement from the Kremlin about the telephone call echoed previous statements that Mr. Putin had made about his goals for relations with Washington, including “a return to pragmatic, mutually beneficial cooperation.”

Mr. Putin openly endorses the idea that the world should return to the era when two superpowers assumed a general responsibility for global stability and security.

Some analysts, however, have suggested that Mr. Trump is unpredictable and the traditional Republican penchant for painting Russia as a dire threat could still emerge. The Putin administration is hoping that the West will lift sanctions imposed over the crisis in Ukraine.

On the phone call, which the Kremlin said was arranged by mutual consent, the two men agreed to stay in contact and to meet at an unspecified date in the future.

Earlier, Mr. Trump described the note on his victory that he received from Mr. Putin as “beautiful.”

For its part, Russia has continued its glowing tributes to Mr. Trump as a paragon who triumphed in what is repeatedly depicted in the Russian media as the swamp of American politics. The main weekly news program on state television every Sunday night tends to focus mainly on the United States, with Dmitry Kiselyov, the anchor, suggesting this week that Europe follow the American lead in replacing its leaders.

Under President Trump, Mr. Kiselyov said, the American government would finally drop what the Russian anchor called its annoying slogans about human rights and democracy.

“Russia has a lot of trust in Trump,” he said.

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