Russian President Dmitry Medvedev flew in fresh from talks with Mr Obama in Moscow in which they agreed a framework for new nuclear weapons cuts.
The leaders of France, Canada and Japan are also attending, along with EU representatives.
But Hu Jintao, China's president, cancelled plans to attend the summit and address G8 leaders, instead flying back to Beijing amid continuing unrest in China's western region of Xinjiang.
The summit opened with a working lunch for the leaders, but a draft declaration was already circulating amongst journalists covering the talks.
On the world economy it said: "While there are signs of stabilisation, including recovery in stock markets ... the situation remains uncertain and significant risks remain to economic and financial stability."
Other points reported to be in the draft communique include:
G8 leaders will agree that the global economy is too shaky to begin rolling back massive fiscal stimulus plans
The G8 is seeking to conclude the stalled Doha round of trade talks with developing nations by 2010
The world's average temperature should not rise by more than 2C (3.6F)
Gender equality will be promoted as a "key issue for aid effectiveness and to reduce poverty"
The statement echoed an assessment by the IMF on Wednesday which said the world economy was beginning to pull out of recession, but recovery was likely to be uneven and sluggish.
The IMF says problems in financial markets and banks remain, and developed economies are unlikely to resume growth until the second half of next year.
On climate change, an EU official told AFP news agency that the G8 had dropped a pledge to cut global greenhouse gas emissions by 50% by 2050.
"There is a very strong commitment to identify the global goal for substantially reducing global emissions by 2050, but there is no 50%," the official said.
G8 leaders are under pressure to get closer to a new deal on climate change management ahead of a crucial meeting in Copenhagen in December.
Italian Prime Minister Silvio Berlusconi moved the summit to L'Aquila to show solidarity with the victims of April's earthquake.
He took Mrs Merkel on a tour of Onna, a nearby village almost flattened by the quake, and Mr Obama was later given a tour of L'Aquila.
Germany has pledged to help rebuild the church in Onna as a symbol of reconciliation for a massacre of 17 villagers by German troops in 1944.
"The world has changed. We have become friends with the people (of Onna) and Germany can help," Mrs Merkel said.
Mr Berlusconi may also be hoping to use the summit to put his domestic troubles behind him. His wife has filed for divorce and he has faced myriad accusations about wild parties and relations with young women and prostitutes.
Officials will also be hoping for more positive headlines than when Italy hosted the G8 in Genoa in 2001. That summit was marred by violent protests and police faced charges of brutality and misconduct.
Inside the G8 nerve centre
But on Tuesday, police in Rome said they had arrested 36 people after masked protesters blocked roads, threw objects and set fire to tyres.
On Wednesday, dozens of protesters occupied four coal power plants in different regions of Italy, demanding tougher measures from G8 leaders in fighting climate change, Greenpeace said.
International political issues like the Iranian election aftermath, the Middle East, nuclear weapons and terrorism will also feature in talks.
African leaders will join the three-day summit on Friday to push for a new initiative to fund farming in the developing world and tackle global hunger.
The financial crisis has had a severe impact in some developing countries and campaign groups say it makes it all the more important for the G8 to live up to earlier commitments to increase aid, the BBC's Andrew Walker in L'Aquila says.
LOCATION OF 2009 G8 SUMMIT
L' Aquila was at the epicentre of a major earthquake that hit the Italian region of Abruzzo on 6 April this year.
The G8 summit is being held at the Guardia di Finanza non-commissioned officers' school. This was where the funeral of the earthquake victims took place and also the HQ of the department co-ordinating emergency work.
The barracks comprise more than 50 buildings. World leaders are staying in the officers' quarters and more than 2,400 journalists are housed in a "media village".
April's earthquake damaged several medieval buildings, including the church of Santa Maria di Collemaggio. A statue of the Virgin Mary and Child (pictured) recovered from the church is on display at the G8 venue among other works of art affected by the quake.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.