Terrorism will be top of the agenda at Thursday's meeting in Brussels which comes amid sharp divisions.
Terrorism will be top of the agenda at Thursday's meeting in Brussels which comes amid sharp divisions over joining the US-led coalition against the Islamic State group.
"I expect NATO allies to step up and agree to do more in the fight against terrorism, not least because of the attack we saw in Manchester," Stoltemberg told a news conference on the eve of the summit.
Trump arrives in Brussels later Wednesday having said NATO was "obsolete" because it did not focus on the threat of Islamist terrorism.
He has since softened the criticism but still wants NATO to join the anti-IS coalition itself as an important gesture of support for the campaigns in Syria and Iraq.
All 28 allies have joined the coalition as individual countries and if NATO became a member, that would significantly boost coordination in the war against IS in Syria and Iraq, Stoltenberg recalled.
He said the "brutal attack" claimed by IS showed the terror threat remained ever present.
"Many allies would like to see NATO as a full member of the coalition," Stoltenberg added.
"Firstly, because it sends a strong message of unity... and especially in light of the attack in Manchester, I think it is important to send this message of unity against terrorism," he said.
NATO currently provides AWACS surveillance planes to help anti-IS operations and trains officers in Iraq but it stresses that these are and should remain non-combat roles.
Diplomatic sources say some of the allies, including France and Germany, are reluctant to go further for fear of getting dragged into a ground war and risking NATO's standing with Arab powers.
They are also concerned NATO could end up taking over control of the whole operation in Iraq.
New French President Emmanuel Macron is due to meet Trump for lunch Thursday when the issue is expected to be a major talking point.