"I recently spoke with President Obama on the phone. We spoke twice and we had long, substantial conversations," Putin said in an appearance with Kerry before their meeting. "I had a chance to discuss many aspects of our relations. I got his letter.
"I hope to be able to meet with Mr. President shortly in person. We will have a number of opportunities this year. I think it's very important that our key ministries and agencies, including the Foreign Ministry, cooperate in finding solutions for the most topical and relevant issues of today's world."
Kerry responded in kind, telling the Russian leader "you know better than anybody, there are enormous challenges today that require the same level of cooperation."
Kerry said the United States appreciates Russia's cooperation in investigating the Boston Marathon bombing.
Kerry said Obama,, who "is looking forward to seeing" Putin at an upcoming Group of Eight meeting in Ireland, "would reiterate that there are many issues -- economic, economic cooperation, the challenges of North Korea, Iran, Syria and many other issues -- of which he believes that we could cooperate very significantly."
Kerry also said the United States and Russia "share some very significant common interests with respect to Syria -- stability in the region, not having extremists creating problems throughout the region and elsewhere."
"So it's my hope that today we'll be able to dig into that a little bit and see if we can find the common ground," Kerry said.
Prior to Kerry's arrival, a senior U.S. State Department official said Kerry was expected to have a "serious conversation on Iran, North Korea, Afghanistan and finally, without question, we'll be discussing Syria."
"I fully expect a serious dialogue on issues of trade and cooperation," the official, speaking anonymously, said. "Both President Putin and President Obama ... have made clear that they want to see more activity in terms of our bilateral relationship in this dimension, and so this trip will give us an opportunity to discuss some of the ideas that we've outlined in that sphere."
Kerry and Russian leaders also will discuss counter-terrorism cooperation, the official said.
Kerry also was to meet with Foreign Minister Sergei Lavrov.
Kerry's two-day trip to Russia is his first since he was confirmed as secretary of state.
Kerry flew to Moscow Monday. On Wednesday, he will travel to Rome, where he will meet with senior Italian government officials to discuss bilateral and global issues, including events in Afghanistan, Syria, and elsewhere in the Middle East, the State Department said.
While in Rome, Kerry will meet with Jordanian Foreign Minister Nasser Judeh to discuss regional issues and with Israeli Justice Minister Tzipi Livni as part of his discussions on peace in the Middle East, the department said.