NATO defence ministers are meeting over two days at the alliance's Brussels headquarters as US President Donald Trump arrived in Beijing to press key player China to do more to get Pyongyang to curb its nuclear and ballistic weapons programmes.
The North Korean nuclear crisis will be the focus of a working dinner today, where ministers will be joined by the EU's diplomatic chief Federica Mogherini.
"All NATO allies agree that we have to put strong pressure on North Korea because North Korea is responsible for reckless behaviour, irresponsible behaviour developing nuclear weapons and by developing missiles," Stoltenberg said.
"We have to put pressure on North Korea to reach a peaceful negotiated solution. Pressure is the path to peace."
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Today's talks will also look at efforts to revamp NATO's command structure to help it better combat the rising threat from Russia.
As he flew to Europe, Mattis told reporters that coalition partners are looking to the United States for a clear plan about what follows the physical defeat of IS.
"Maybe three-quarters of the questions I am getting asked now is (about) going forward. It's not about are we going to be able to stop ISIS, are we going to be able to overcome ISIS. They are now saying: 'What's next? How is it looking?'" Mattis said.
America's military involvement in Syria has until now been focused solely on fighting IS, but with the jihadists on the ropes, Washington must articulate its longer-term interests and what role, if any, US forces will play in Syria.
Mattis supports a UN-backed effort in Geneva, which has run in parallel to a Russian and Iranian-led process, to reach a diplomatic solution.
America has armed and trained Kurdish and Syrian Arab fighters who are battling IS on the ground, but the weapons provided to the Kurdish YPG are a source of huge angst for NATO ally Turkey, which views the group as terrorists.
NATO has been in Afghanistan since the US-led invasion in late 2001 to dislodge the Taliban in the wake of the September 11 attacks.
Despite a 16-year war and hundreds of billions of dollars in investment in Afghan institutions and security forces, the country remains beset by corruption and an ongoing security crisis that is killing thousands of local soldiers and civilians each year.
According to diplomatic sources, the US would contribute around 2,800 troops, while other NATO allies and partner countries would supply around 700 more.
Mattis arrived in Brussels from Helsinki, where he attended a forum called the Northern Group, a little-known meeting of northern European nations focusing on the continent's military and security challenges, particularly from Russia.
Moscow frequently sends warplanes into the skies around the Baltics, and Europe remains anxious about Russia's military intentions, especially after the 2014 annexation of Crimea from Ukraine.