Chancellor Angela Merkel wants the group to reach an agreement on limiting global temperature rises.
She is also calling on the G7 members to contribute to a fund for poor countries suffering the worst consequences of climate change.
There are also talks on the threat from radical extremism with the leaders of Nigeria, Tunisia and Iraq.
The summit is being held at the picturesque Schloss Elmau hotel in Kruen in the Bavarian Alps.
The leaders of the US, UK, Japan, France, Canada and Italy are attending the talks, hosted by Ms Merkel.
The first working session on Monday focused on climate and energy, with Chancellor Merkel trying to get leaders to agree to keeping temperature rises within 2C of pre-industrial levels.
She is hoping to secure commitments from her G7 guests on tackling global warming to build momentum before a major United Nations climate summit in Paris in December.
G7 leaders were then 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 (IS) and Boko Haram.
On Sunday, Prime Minister 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.
IS 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.
Climate change and terrorism are top of the agenda on the second day of the G7 summit of economic powers in Germany.