"And if we're not willing to do that, we're not going to get a good deal", Graham said, complementing the global community - including China and Russian Federation - for standing behind Trump in regards to sanctions on North Korea.
After their historic meeting, President Trump shows North Korean dictator Kim Jong Un a sneak peek inside the presidential limo. "I think it will be tremendously successful, and it's my honor and we will have a terrific relationship".
Mr Trump added: "I learned he's a very talented man".
Elsewhere scores of people were glued to TV screens at the Seoul railway station, cheering and clapping in response to Trump and Kim's cordial greetings.
Trump described Kim as a "very worthy, very smart negotiator".
South Korea said last month the issue of USA troops stationed there was unrelated to any future peace treaty with North Korea and that American forces should stay even if such an agreement were signed.
Earlier the two leaders shook hands and posed for photographs, before moving inside the hotel to talk to reporters.
Answering questions at a press conference at the Capella Hotel on Singapore's resort island of Sentosa, where his meeting with Kim took place, Trump said bringing home USA soldiers stationed in South Korea is now not part of the equation. "Did Kim Jong-un just make a vague Iron Sky reference?"
Language on North Korea's bombs was similar to what the leaders of North and South Korea came up with at their own summit in April.
Singapore's Ministry of Foreign Affairs (MFA) released a statement saying the two discussed mutual relations and the situation on the Korean peninsula, with Prime Minister Lee thanking Kim for his and Trump's "bold and admirable decision" to hold the summit.
With reference to the Korean war Trump said.
After briefly moving away from the media glare, Mr Kim and Mr Trump reappeared, walking together along a balcony and posing for pictures.
When asked about denuclearisation, Trump said: "We are starting the process very quickly".
Should they succeed in making a diplomatic breakthrough, it could bring lasting change to the security landscape of Northeast Asia, like the visit of former U.S. President Richard Nixon to China in 1972 led to the transformation of China.
The interpreter of North Korean leader Kim Jong-un for his summit with U.S. President Donald Trump had a daunting task to perform as he translated Trump's notoriously free-associating verbal style for his boss.
The summit, which was nearly scrapped by a mercurial Trump last month, comes after a flurry of diplomatic activities and barrage of invective and insults traded between the US President and an equally aggressive Kim.