Graham made the remarks after saying he agreed with Democrats' demands in letter to President Donald Trump that any nuclear agreement meet several standards, including requiring North Korea to denuclearize, scrap its ballistic missile program and allow robust inspections, before any easing of sanctions.
Sporadic provocations by the North have continued while Pyongyang has made increasing advances in its nuclear arsenal, which it says it needs to defend against the risk of a USA invasion.
"When I woke up this morning I saw the news in the newspaper that our respected Marshal went to Singapore for the North Korea-U.S. summit", said Han Il Gwang, a Pyongyang resident, displaying typical discretion when speaking to an Associated Press Television crew.
Kim was the first to arrive in Singapore, landing at Changi airport on a commercial Air China plane, after intense speculation with the public tracking three separate aircraft leaving Pyongyang, the North Korean capital.
Kim's North Korean delegation will include his sister Kim Yo Jong, White House officials cited by Bloomberg noted.
The two leaders are scheduled to meet for the first time on Tuesday at the Capella Hotel on Sentosa Island, where the process regarding denuclearisation of North Korea may kick-start in exchange for economic aid. He said he thinks "it's going to work out very well". One dispatch by the Korean Central News Agency said North Korea and the United States would exchange "wide-ranging and profound views" on establishing new relations, building a "permanent and durable peace-keeping mechanism", achieving denuclearization and "other issues of mutual concern, as required by the changed era". While foreign policy isn't usually a major aspect of congressional elections, it is unclear if Trump's focus on getting tough with trade partners and solving the Korean Peninsula issue will have some influence on voters in the mid-term polls in November.
Trump landed in Singapore a little after 8:30 p.m. local time for the highly-anticipated meeting with the North Korean leader, which is set to take place on Tuesday.
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Trump had called Kim "Little Rocket Man" and threatened to unleash "fire and fury like the world has never seen" on North Korea as it conducted several ballistic missile tests in defiance of global warnings.
Mr Trump and Mr Kim have had an extraordinary up-and-down relationship over the past 18 months, trading insults and threatening war before abruptly changing tack and moving towards a face-to-face meeting.
Singapore Foreign Minister Vivian Balakrishnan shared a photo that showed him Balakrishnan welcoming Kim Jong-Un to Singapore.
"The entire world is watching the historic summit between (North Korea) and the United States of America, and thanks to your honest efforts. we were able to complete the preparations for the historic summit", Kim told Lee through an interpreter.
It's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes.
North Korean soldiers keep watch toward the south in the village of Panmunjom, South Korea, on April 17.
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 U.S. -led U.N. troops backing Seoul against Pyongyang's forces that were aided by China.
"They will use [nuclear weapons] first against us, and then with the long-range missiles that they're building and that the deal doesn't prevent them from building, against everyone else", Netanyahu said.