German Chancellor Angela Merkel wants the economic powers group to reach an agreement on limiting global temperature rises.
Angela Merkel also wants G7 members to contribute to a fund for poor countries suffering the worst effects of climate change.
There will also be talks on the threat from radical extremism with the leaders of Nigeria, Tunisia and Iraq.
G7 summit is being held at the picturesque Schloss Elmau hotel in Krun in the Bavarian Alps.
It is being attended by President Barack Obama, UK PM David Cameron, Japanese PM Shinzo Abe, French President Francois Hollande, Canadanian PM Stephen Harper and Italian PM Matteo Renzi.
The first working session on June 8 will focus on climate and energy, with Chancellor Angela Merkel trying to get leaders to agree to keeping temperature rises within 2C of pre-industrial levels.
Angela Merkel is hoping to secure commitments from her G7 guests on tackling global warming to build momentum before a major UN climate summit in Paris in December.
Later, G7 leaders will be joined by Iraqi PM Haider al-Abadi, Nigerian President Muhammadu Buhari and Tunisian President Beji Caid Essebsi to discuss the threat posed by groups like Islamic State (ISIS) and Boko Haram.
On June 7, David Cameron said the UK was sending an extra 125 military trainers to Iraq to help in the battle against IS, describing the militants as “the biggest threat” G7 leaders had to address.
ISIS continues to control large swathes of Iraq and Syria despite being the target of a US-led air campaign against them.
In Nigeria, a similar regional battle is being fought against Boko Haram militants who have carried out attacks since 2009 to try to create an Islamic state.
The 41st G7 summit is held in Schloss Elmau, Krün, Bavaria, Germany on June 7–8, 2015.
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