Key items on the agenda are taxation, transparency and counterterrorism.
The issue of Syria was discussed on Monday evening at a meeting between Russian President Vladimir Putin and U.S. President Barack Obama and also at a working dinner later.
Putin and Obama admitted they had big differences on Syria, but they agreed to push for a summit in Geneva, Switzerland.
"Our positions do not fully coincide, but we are united by the common intention to end the violence, to stop the number of victims increasing in Syria, to resolve the problems by peaceful means, including the Geneva talks," said Putin at a joint press conference with Obama.
"We agreed to push the process of peace talks and encourage the parties to sit down at the negotiation table, organize the talks in Geneva," he said.
The United States announced it would begin arming Syria's opposition forces because it has proof chemical weapons were used against the rebels. But Russia has dismissed the claims, saying they're based on flimsy evidence.
British Prime Minister David Cameron described Monday evening's discussions on Syria as "encouraging."
He is also looking for an agreement on ways that the government can get more tax information from offshore tax havens like Bermuda, the Cayman Islands or the Isle of Man.
The G8 leaders will also be addressing counter-terrorism at their morning session.
The first day of the summit saw a launch of formal negotiations on a free trade agreement between the European Union (EU) and the United States.
The summit is taking place amid intensive security at the Lough Erne resort and its outskirts, with 8,000 police on duty around the venue.
--ANI (Posted on 19-06-2013)