He said he asked the Russian leader if he interfered in the 2016 USA election and received assurances from Mr Putin that he "absolutely did not meddle".
"Might be a odd thing to happen but it's certainly a possibility", Trump said during a press conference with Vietnam's president, adding that it would be "very, every nice if it did".
She said she was protesting against Donald Trump's attitude to women and his failure to meet with human rights activists in Vietnam.
He said the US wouldn't threaten Kim if he gave up his nuclear weapons.
"Strange things happen in life".
Trump has been working to rally global pressure against North Korea's nuclear weapons program on the trip to Asia.
Mueller Intensifying Pressure in Flynn Investigation, Has Enough Evidence to Charge
Another former Trump campaign aide, George Papadopoulos, has pleaded guilty to lying to the Federal Bureau of Investigation . The anti-Trump media appears to have quite the connection to the investigation led by Special Counsel Bob Mueller.
Trump, 71, sarcastically responded that he hopes one day to be friends with Kim, who oversees a developing nuclear weapons and ballistic missile arsenal.
North Korean officials described Trump's trip as "nothing but a business trip by a warmonger to enrich the monopolies of the United States defense industry".
Those comments drew sharp criticism in Washington, where Rep. Adam Schiff (D-Calif.), the ranking member of the House Permanent Select Committee on Intelligence, said the president understands the truth about Russian interference, and is simply choosing to accept Putin's denials "over the solid evidence of our own intelligence agencies".
Utilising Twitter's new 280-character tweet length Mr Trump gave his thoughts on a range of subjects, from relations with Russia, China's efforts to rein in North Korea, and a sarcastic message about his bid to make "a friend" of Kim.
The US think-tank said: "Although Pyongyang is outspent by its neighbours in dollar-to-dollar comparisons and defence experts say it operates with raging equipment and technology, the regime's forward-deployed military position and missiles aimed at Seoul ensure that Pyongyang's conventional capabilities remain a constant threat to its southern neighbour".
We'll see what happens now.
The secretive kingdom's state-controlled media service told the North Korean people today how their former countrymen south of the Demilitarised Zone are suffering "untold pains under the U.S. occupation and domination".
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