U.S. Secretary of State John Kerry has called on Russian President Vladimir Putin to help find "common ground" with Washington over the conflict in Syria.
Kerry held an extended meeting with Putin and his Russian counterpart Sergei Lavrov in the Kremlin on May 7.
He and Lavrov made short press statements before heading back into more talks.
Kerry expressed hope Russia and the United States will stand together on "some significant challenges," and mentioned Syria and the Middle East among them.
"I come here on [U.S. President Barack Obama's] behalf committed to the notion that Russia and the United States can cooperate on some significant challenges that we face now and make a very real contribution to the possibilities of stability and peace in places like the Middle East, Syria, and other challenges that we face," Kerry said.
"So I look forward to continuing our conversation and hopefully we'll have more to announce to the press at the end of those conversations."
Lavrov said that, while there were still disagreements between the two sides, the talks were promising.
"We had a very saturated day. We just held our meeting in the Kremlin with the president of the Russian Federation and I would like to once again express our satisfaction with the tone and the atmosphere of the rich and useful conversation that we had," Lavrov said.
"I believe that one of the most important conclusions of the meeting with the president of the Russian Federation is the mutual wish to do everything in order to overcome the legacy of the past once and for all and to further improve trust between our countries as a precursor of a fruitful partnership in bilateral and international agenda," he continued.
"Certainly, we still have problems in our relations, however, with resolve like that we will be consistent in solving them."
Kerry arrived on May 7 in Moscow for his first visit since becoming the United States' top diplomat in January.
For more than a year, U.S. efforts to sway Russia on Syria have largely fallen on deaf ears, with the Kremlin denouncing any steps it sees as precursors for foreign intervention.
Russia and China have blocked bids for toughened UN action against Damascus. Moscow has continued to funnel weapons to the regime, even as the death toll has soared past 70,000.
Washington has been critical of the deepening crackdown on NGOs under Putin, including legislation mandating that they register as "foreign agents" if they receive funding from the United States or other countries.
The visit also follows April's terror attack in Boston, allegedly perpetrated by two ethnic Chechen immigrants, which has led to renewed focus on counterterrorism cooperation.
On May 8, Kerry will meet members of Russia's beleaguered civil society at the home of U.S. Ambassador Michael McFaul.
Kerry started his visit by laying a wreath at the Tomb of the Unknown Soldier near the Kremlin.
UN Peacekeepers Held
Meanwhile in Syria, rebel forces say they are holding four Filipino UN peacekeepers on the cease-fire line between Syria and the Israeli-occupied Golan Heights after clashes in the area had put them in danger.
The Yarmouk Martyrs Brigade posted a statement on its Facebook page on May 7 accompanied by a picture of four peacekeepers wearing light-blue UN flak jackets marked "Philippines."
UN Secretary-General Ban Ki-moon strongly condemned the detention and called for the peacekeepers' immediate release.
They were detained as they patrolled close to an area where 21 Filipino observers were held for three days in March.
The same group was responsible for the March incident and initial reports described it as hostage-taking, which the rebel unit denied.
With reporting by Media.mid.ru, ITAR-TASS, Interfax, Reuters, AP, and AFP