The conspicuous shift on Syria has benefits for both countries.

It has given Russia the opportunity to reassert its view of geopolitics, arguing against international efforts to remove undesirable governments from power, as the United States and its allies did in Libya. It has also allowed the Obama administration to defer, for now, calls for the United States to act more forcefully to intervene in the Syrian conflict.

Mr. Kerry’s focus on Russia and its role in Syria reflects a decision by the White House to pull relations with Russia back from the brink in President Obama’s second term. The first term included a honeymoon that Mrs. Clinton called a reset, which led to reductions in nuclear weapons and Russia’s ascension to the World Trade Organization, among other things.

Tensions erupted, though, over the Arab spring, the overthrow of Libya’s dictator, Muammar al-Qaddafi, and ultimately Mr. Putin’s own return to the presidency in elections widely denounced as undemocratic.

Mr. Putin, as a candidate and as president once again, adopted stridently anti-American views. After the disputed parliamentary elections of 2011, he accused Mrs. Clinton of personally instigating large protests in Moscow. Russia subsequently ended more than two decades of collaboration with the United States Agency for International Development, labeled legally defined nongovernment organizations receiving American assistance as “foreign agents”; and after the United States imposed sanctions on Russian officials under new legislation named after a lawyer who died in prison, Sergei Magnitsky, it barred adoptions of Russian children by American parents.

All of those actions have made Mr. Kerry’s personal outreach to Mr. Lavrov even more striking. Since being sworn in, Mr. Kerry has met with Mr. Lavrov five times — in Berlin, London, Brussels, Moscow and Kiruna, Sweden, where they talked one-on-one for an hour on the sidelines of a meeting of the Arctic Council this week to work out details of the coming negotiations over Syria. The five meetings are the most Mr. Kerry has had with any foreign diplomat, exceeding his four with Turkey’s foreign minister, Ahmet Davutoglu.

Mr. Kerry and Mr. Lavrov, according to one official familiar with their exchanges, have developed a rapport. In Moscow, they bantered about “their mutual love for hockey and the grace of the older school style.” The two men left their delegations inside the Foreign Ministry’s guesthouse and strolled through the mansion’s gardens, engaging in a lengthy — at times animated — discussion over the exact wording of the statement they announced later that night.

Mikhail V. Margelov, chairman of the Foreign Affairs Committee of the upper chamber of the Russian Parliament, said that Russia’s position on Syria had been consistent and that Mr. Kerry had finally accepted it.