The Republican nominee told a TV interviewer that the Russian president was “very much of a leader” who has “very strong control over his country”.
Mr Trump and his Democratic rival Hillary Clinton were being quizzed separately on national security and military matters at a so-called Commander in Chief forum.
Speaking about Russia and Mr Putin’s position, he said: “It’s a very different system, and I don’t happen to like the system. But certainly in that system he’s been a leader, far more than our president has been a leader.”
Mr Obama responded while on an overseas visit by condemning Mr Trump as unsuitable to be commander-in-chief.
He said: “I don’t think the guy’s qualified to be president of the United States and every time he speaks, that opinion is confirmed.”
Mr Trump’s comments follow a pledge that he would get his generals to provide a plan to defeat Islamic State within 30 days.
Mr Putin is helping his ally Bashar al Assad by providing military support for the Syrian regime in their civil war against rebels and militants including IS.
But there have been suggestions he has been conducting secret ground wars both in Syria and Ukraine.
NBC’s Matt Lauer also asked Hillary Clinton why she should not be disqualified from running after using a private server to handle government emails while Secretary of State.
Mrs Clinton, while stressing she had not improperly handled classified information, said: “It was a mistake to have a personal account. I would certainly not do it again. I make no excuses for it.”
The forum, which was held on board the aircraft carrier USS Intrepid, did not see Mr Trump and Mrs Clinton go head to head.
The first debate between them is scheduled for 26 September.
Earlier, Mr Trump pledged to increase US military spending – already much higher than any other nation – with an active army of about 540,000 troops, an air force of at least 1,200 fighter jets and a navy of 350 ships.
But he failed to say how it would be funded.
When asked how he expected to defeat IS, Mr Trump was vague, responding he didn’t “want to broadcast to the enemy what my plan is”.
The US has for the last two years been leading an international coalition, including the UK, carrying out airstrikes in support of local forces on the ground in the battle against IS.
Lauer asked Mr Trump whether he would ask the same generals to devise an IS plan as those he had previously criticised for knowing less than him about the militant group.
Mr Trump replied: “Well, they’d probably be different generals, to be honest with you.”
The Republican nominee went on to reveal that, during an apparently secret security briefing, he had been told Mr Obama had not followed the recommendations of his advisers.
He said: “I did learn that our leadership – Barack Obama – did not follow what our experts and our truly – when they call it intelligence, it’s there for a reason – what our experts said to do.”
News Source SkyNews