But Sajjan says it's too early to say when a Canadian-led North Atlantic Treaty Organisation training mission in Iraq will resume.
At a meeting of North Atlantic Treaty Organisation defense ministers in Brussels it was agreed North Atlantic Treaty Organisation will take over some of the training activities carried out by the American-led coalition against the Islamic State.
Trump stoked speculation about a bigger North Atlantic Treaty Organisation footprint in the Middle East a month ago after Iran carried out attacks in Iraq on two bases used by American troops as retaliation for a USA airstrike that killed top Iranian General Qassem Soleimani in Baghdad.
Defense ministers also discussed the situation in the wider Middle East and agreed to "strengthen" the security forces in Afghanistan.
North Atlantic Treaty Organisation ministers, including U.S. Defense Secretary Mark Esper, will also discuss more options for the alliance in the Middle East in a bid to mollify Trump, a sharp critic who has accused some allies of being "delinquent" because they do not spend enough on defence.
Stoltenberg, speaking at a news conference at the end of the first day of a two-day meeting, pointedly said the "enhanced" North Atlantic Treaty Organisation presence in Iraq "would be with the consent of the Iraqi government".
Stoltenberg provided no details of how many troops might shift to the current training force numbering about 500 or what new activities they might eventually undertake.
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"I wouldn't talk about more or less troops", he said. A second step, possibly over the summer, would see the mission's mandate changed to take over more activities now handled by the coalition.
He added, "This is why we are considering taking on some of the coalition's current training activities".
"As a result of the letter of response from Iraq over the course of the last 36 hours, we will now recommence the NATO Mission Iraq", Wolters told reporters at the Munich Security Conference.
"Everything we do in Iraq will be in close coordination and with the consent of the Iraqi government", he said.
The aim of the expanded training mission, he went on, "is to increase the capacity of Iraq's armed forces so that they no longer need our support in the fight against terrorism and to ensure that ISIS does not come back".
Sajjan did indicate that a group of military engineers who have been training Iraqi forces on how to disarm explosives through the US -led coalition could be rolled into the North Atlantic Treaty Organisation mission. It cast uncertainty over the future of not only the North Atlantic Treaty Organisation mission, but the entire global effort against the Islamic State of Iraq and the Levant. No additional personnel would be deployed to the strife-torn country.