MOSCOW, Nov 14 (Reuters) - Russian President Vladimir Putin and U.S. President-elect Donald Trump on Monday agreed to work towards "constructive cooperation," including on fighting terrorism, the Kremlin said.
In their first phone call since Trump won the Nov. 8 election, they agreed to "channel" relations between Russia and the United States and "combine efforts to tackle international terrorism and extremism."
"The importance of creating a solid basis for bilateral ties was underscored, in particularly by developing the trade-economic component," the Kremlin said in its statement.
See images of Obama and Putin throughout the years:
Obama and Putin's awkward meetings through the years
Obama and Putin's awkward meetings through the years
FILE - In this Monday, Nov. 16, 2015 file photo, U.S. President Barack Obama, right, talks with Russian President Vladimir Putin, left, prior to a session of the G-20 Summit in Antalya, Turkey. The tide of global rage against the Islamic State group lends greater urgency to ending the jihadisâ ability to operate at will from a base in war-torn Syria. That momentum could also force a reevaluation of what to do about President Bashar Assadâs future and puts a renewed focus on the position of his key patrons, Russia and Iran. (Kayhan Ozer/Anadolu Agency via AP, Pool, File)
Russian President Vladimir Putin, left, and U.S. President Barack Obama shake hands at the COP21 UN Conference on Climate Change in Paris, France, Monday, Nov. 30, 2015. (Mikhail Klimentyev/Sputnik, Kremlin Pool Photo via AP)
United States President Barack Obama, right, and Russia's President President Vladimir Putin pose for members of the media before a bilateral meeting Monday, Sept. 28, 2015, at United Nations headquarters. (AP Photo/Andrew Harnik)
U.S. President Barack Obama, right, gestures while speaking to Russian President Vladimir Putin before a bilateral meeting at United Nations headquarters in New York, Monday, Sept. 28, 2015. (Mikhail Klimentyev, RIA-Novosti, Kremlin Pool Photo via AP)
Russian President Vladimir Putin, right, passes by US President Barack Obama at the Asia-Pacific Economic Cooperation (APEC) Summit, Tuesday, Nov. 11, 2014 in Beijing. (AP Photo/RIA Novosti, Presidential Press Service)
Leaders pose for a group photo at the Asia-Pacific Economic Cooperation (APEC) summit at the International Convention Center in Yanqi Lake, Beijing, on Tuesday, Nov. 11, 2014. Among those pictured are, left to right: Brunei's Sultan Hassanal Bolkiah; Papua New Guinea Prime Minister Peter O'Neil; Indonesia's President Joko "Jokowi" Widodo; Japanese Prime Minister Shinzo Abe; U.S. President Barack Obama; Australian Prime Minister Tony Abbott; Chinese President Xi Jinping; Malaysia Prime Minister Najib Razak; Russian President Vladimir Putin; New Zealand Prime Minister John Key. (AP Photo/Ng Han Guan)
BEIJING, CHINA - NOVEMBER 10: U.S. President Barack Obama (L) and Russian President Vladimir Putin (R) attend a family photo ceremony during the APEC Leaders meeting November 10, 2014 in Beijing, China. The APEC Summit hosted 1500 economic leaders in Beijing to deliberate key issues facing the Asia-Pacific economy. (Photo by Sasha Mordovets/Getty Images)
SAINT PETERSBURG - SEPTEMBER 05: U.S. President Barack Obama (R) greets Russian President Vladimir Putin at the G20 summit on September 5, 2013 in St. Petersburg, Russia. The G20 summit is expected to be dominated by the issue of military action in Syria while issues surrounding the global economy, including tax avoidance by multinationals, will also be discussed during the two-day summit. (Photo by Sasha Mordovets/Getty Images)
Russia's President Vladimir Putin, left, shakes hands with U.S. President Barack Obama during arrivals for the G-20 summit at the Konstantin Palace in St. Petersburg, Russia on Thursday, Sept. 5, 2013. The threat of missiles over the Mediterranean is weighing on world leaders meeting on the shores of the Baltic this week, and eclipsing economic battles that usually dominate when the G-20 world economies meet. (AP Photo/Dmitry Lovetsky)
Russias President Vladimir Putin (L) walks past US President Barack Obama as he arrives to pose for the family photo during the G20 summit on September 6, 2013 in Saint Petersburg. World leaders at the G20 summit on Friday failed to bridge their bitter divisions over US plans for military action against the Syrian regime, with Washington signalling that it has given up on securing Russia's support at the UN on the crisis. AFP PHOTO / JEWEL SAMAD (Photo credit should read JEWEL SAMAD/AFP/Getty Images)
FILE - In this Monday, June 17, 2013 file photo President Barack Obama meets with Russian President Vladimir Putin in Enniskillen, Northern Ireland. In an interview with the Associated Press on Tuesday Sept. 3, 2013 Putin sought to downplay the current chill in the U.S.-Russian relations and said that the two countries need to cooperate on a range of issues in the interests of global stability. (AP Photo/Evan Vucci, File)
FILE - In this June 17, 2013, file photo, President Barack Obama meets with Russian President Vladimir Putin in Enniskillen, Northern Ireland. The White House is considering canceling a fall summit between President Barack Obama and Russian President Vladimir Putin in Moscow, a move that would further aggravate the already tense relationship between the two leaders. The White House is dangling that option over the Russians as Moscow considers a temporary asylum petition from Edward Snowden, the American accused of leaking information about classified U.S. intelligence programs.(AP Photo/Evan Vucci, File)
ENNISKILLEN, NORTHERN IRELAND - JUNE 18: Leaders (L-R) Russia's President Vladimir Putin, Britain's Prime Minister David Cameron, US President Barack Obama stand for the 'family' group photograph at the G8 venue of Lough Erne on June 18, 2013 in Enniskillen, Northern Ireland. The two day G8 summit, hosted by UK Prime Minister David Cameron, is being held in Northern Ireland for the first time. Leaders from the G8 nations have gathered to discuss numerous topics with the situation in Syria expected to dominate the talks. (Photo by Matt Cardy/Getty Images)
G8 leaders from center rear clockwise, Britain's Prime Minister David Cameron, US President Barack Obama, French President Francois Hollande, Canadian Prime Minister Stephen Harper, Italian Prime Minister Enrico Letta, European Council President Herman Van Rompuy, European Commission President Jose Manuel Barroso, Japan's Prime Minister Shinzo Abe, German Chancellor Angela Merkel and Russian President Vladimir Putin attend a working session during the G-8 summit at the Lough Erne golf resort in Enniskillen, Northern Ireland on Tuesday, June 18, 2013. (AP Photo/Yves Herman, Pool)
FILE - In this June 18, 2012, file photo President Barack Obama and Russiaâs President Vladimir Putin, left, go to shake hands during their bilateral meeting at the G20 Summit in Los Cabos, Mexico. In a few days' worth of opportunistic diplomacy, Vladimir Putin has revived memories of an era many thought long gone, where the United States and Soviet Union jostled for influence in a Middle East torn between two powers. Whatever happens with its proposal to relieve Syria of chemical weapons, Russia reemerges as a player in the region _ and one who does not easily abandon allies. That's meaningful in a region where America's dumping of Hosni Mubarak has emerged as a seminal moment _ and it may resonate with Iran, whose leaders are carefully watching the global chessboard as the clock ticks toward another showdown, over their nuclear program.(AP Photo/Carolyn Kaster, File)
U.S. President Barack Obama, right, reacts while listening to Russia's President Vladimir Putin before the opening of the first plenary session of the G-20 Summit in Los Cabos, Mexico, Monday, June 18, 2012. (AP Photo/Andres Leighton)
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It added that the countries should "return to pragmatic, mutually beneficial cooperation, which would address the interests of both countries as well as stability and safety the world over."
Trump's team issued a statement saying Putin called to offer congratulations. The statement said Trump told Putin he was looking forward to a strong and enduring relationship with Russia and its people.
The two men will maintain contact by phone and seek to meet each other in person, the statement said.
Trump will succeed President Barack Obama on Jan. 20. Obama's relations with Putin have become tense over issues that include Syria and Ukraine.
(Reporting by Vladimir Soldatkin in Moscow and Steve Holland in Washington; Editing by Robin Pomeroy and Howard Goller)