"The parties agreed with the need to intensify bilateral contacts. It was stated that there is a wish to exchange visits," Kremlin spokeswoman Natalia Timakova said after the two leaders met Friday between G8 summit sessions in Canada, ITAR-Tass reported.
During the hourlong meeting, the two leaders, who previously had spoken only by phone, talked about issues including bilateral relations, the Mideast, Iran, the global recession and the BP oil spill.
"We discussed everything within the framework of G8 and G20, but more importantly, we discussed the current state of affairs in our bilateral relations and agreed that they require certain adjustment," Medvedev said, RIA Novosti reported.
"We are determined to make them more efficient and intense. I hope that our contacts will bring about closer cooperation. We already have such cooperation in certain spheres, and it is useful," he added.
Cameron called the meeting a "real opportunity to put the bilateral relationship on a new footing, to try to make a stronger start and work through the issues where we have agreement and those where we still have things to work through."
RIA Novosti noted Russia-Britain relations have been strained by disputes, including the controversy over the death of former KGB officer Alexander Litvinenko in London in 2006.
The two countries "understand that they are not building their relations from anew, and they have some questions to each other, but this does not mean that Russia and Britain cannot move forward in working together to settle questions in the international arena and expand bilateral economic possibilities," Timakova said.