Asked by Stephanopolous whether Trump deserves credit for brokering the first meeting in recent history between a sitting USA president and a North Korean leader, Menendez said he is anxious Trump "thinks this is a mano-a-mano engagement in which he can achieve the success we want".
A rare direct flight from Pyongyang landed in Singapore on Saturday ahead of the expected arrival of North Korean leader Kim Jong Un for a summit with US President Donald Trump on Tuesday. The North Korean leadership, including Vice Minister of Foreign Affairs Choe Son Hui has also taunted Washington, calling Vice President Mike Pence a "political dummy".
Kim's summit with Trump has captured intense global attention after a turn to diplomacy in recent months after serious fears of war a year ago amid North Korean nuclear and missile tests.
USA and North Korean officials are set to meet Monday morning in Singapore to make final preparations for Tuesday's meeting.
According to Wall Street Journal's Jonathan Cheng, North Korea's main newspaper also covered the leader's trip to Singapore with a front-page photo of Kim boarding the plane.
The United States and North Korea have been in a technical state of war for decades after the eruption of the 1950-1953 Korean War, which pitted USA -led U.N. troops backing Seoul against Pyongyang's forces that were aided by China.
-North Korea summit has shelled out $20 million Singapore dollars, or about $15 million USA dollars, on the historic event, according to Singapore's Prime Minister Lee Hsien Loong.
At the hotel lobby, grim-faced North Korean security guards warned other hotel guests not to take pictures as Kim walked to his Mercedes Benz limousine.
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Word does get around, however, and it is quite likely that the prospect of a meeting between Kim and Trump is on the public's radar.
Ahead of his much-anticipated meeting with Kim, the US President sounded optimistic and said the meeting would be a "one-time shot" at peace.
"Maybe we'll start with the White House", he told reporters after he was asked whether he would invite the North Korean leader to the White House or Mar-a-lago.
"I want, once more, to offer the beloved people of Korea an especial thought of friendship and prayer that the talks, which will take place in the coming days in Singapore, can contribute to the development of a positive path that guarantees a peaceful future for the Korean peninsula and for the whole world", the Pope said in his regular Sunday address. President Trump has described it as a "get-to-know-you situation" and said: "It's going to be a process".
Mr Trump has not approached the North Korea crisis with kid gloves and seems unlikely to adjust his tactics now.
Arriving at the Prime Minister's office after 1900 local time, Kim shook hands with Lee and his staff then sat down to begin talks in front of the cameras before the press was ushered out a few minutes later.
"If a breakthrough is achieved, if peace comes, there will be a bountiful harvest, primarily of course within the Korean Peninsula but indeed for all the rest of us", he said.