The Obama administration wants to find a way to stop the deterioration in U.S.-Russian relations, top Russian officials said here Monday after meeting with Tom Donilon, the U.S. national security adviser.

A letter from President Obama to Russian President Vladimir Putin, conveyed by Donilon, “is written in a constructive tone and has a number of proposals promoting bilateral dialogue and cooperation,” the Russian leader’s foreign policy adviser, Yuri Ushakov, told reporters after the Kremlin get-together.

Ushakov said the White House is sending “positive signals” to Moscow, though he noted that Obama has not moved to tamp down the “Russophobia” in other parts of the American government, by which he meant Congress.

Donilon’s visit occurred after a weekend in which the United States and Russia each released lists of officials from the other country who were being barred from visits. The U.S. list, in compliance with the Sergei Magnitsky Rule of Law Accountability Act, targets 18 people deemed to be human rights violators. They are also subject to financial sanctions. The White House opposed the Magnitsky measure, but it was passed overwhelmingly by Congress.

The Russian list, released a day later, names officials associated with the Guantanamo prison camp and “enhanced interrogation,” as well as prosecutors and judges who have dealt with criminal cases involving several Russians.

Publicly naming people who are barred from entering a country is highly unusual; the Russians have called it provocative. The release of the lists follows a year of unraveling relations between the two countries, which began as Putin reassumed the presidency last spring. Russia has resisted the United States position on Syria, criticized American support for advocacy groups here, expelled USAID and accused Washington of trying to foment rebellion in the streets.

Passage of the Magnitsky law in December led to a Russian ban on American adoptions of Russian children.

Jay Carney, the White House spokesman, said Donilon went to Moscow to discuss a “full range” of issues, including Syria, trade and nuclear non-proliferation. Russia has already been notably critical of North Korean threats against South Korea and the United States.

“We understand we have differences, and we are very clear and transparent and candid about those differences and we engage with Russian officials on those differences,” Carney said. “But we also have areas where we can cooperate in ways that are useful and in the interest of both Russia and the United States.”

“As for us, we shall follow these positive signals,” Ushakov said.

Monday’s talks included, besides Putin, Ushakov and Donilon: U.S. Ambassador Michael McFaul; Rose Gottemoeller, assistant secretary of state for arms control; James Miller, under secretary of defense for policy; Nikolai Patrushev, secretary of the Russian Security Council; Deputy Foreign Minister Sergei Ryabkov; Deputy Defense Minister Anatoly Antonov; and officials from the Russian Federal Security Service and the Foreign Intelligence Service.

Earlier Monday, Donilon met with Foreign Minister Sergei Lavrov. Lavrov afterward told the Itar-Tass news agency that Donilon had reiterated comments made last week by Secretary of State John F. Kerry when he met with him, acknowledging that there were “irritants” in relations between the two countries and pledging to try to ameliorate them.

“Let’s see,” Lavrov said. “We’ll judge by deeds and not by words.”

Scott Wilson in Washington contributed to this story.