Giuliani, in the same remarks in which he suggested Kim had "begged" for a meeting with Trump, said the USA would not meet with North Korea under threat of nuclear war. "We're keeping an eye on negotiations between the North and the USA on the agenda".
The former National Basketball Association star, nicknamed "The Worm", has formed a bromance with North Korea leader Kim Jong-un after a visit to the rogue nation in 2013.
Donald Trump's lawyer Rudy Giuliani has said North Korea's leader "begged" for their summit to be rescheduled after the United States president cancelled it.
On Monday, the White House said the two leaders would start their meeting at 9 a.m. Singapore time on June 12.
Trump's goal in the summit is reportedly to get Kim to agree to a nuclear disarmament schedule, according to the article, and he has been advised not to give up any concessions.
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The U.S. trade deficit, however, fell to a seven-month low in April as exports rose to a record high, the U.S. Trump reportedly responded by saying, "Didn't you guys burn down the White House?" during the May 25 call .
Trump said he didn't want to use the term "maximum pressure" any more, because the two sides were "getting along".
"We will monitor related developments", ministry spokesperson Baik Tae-hyun told reporters.
The confirmation came after the Singapore government earlier in the week made public the cordoning off of the island and surrounding waters as a "special event area", effective from June 10 to June 14.
Mr Trump hopes to secure a nuclear deal with the North Koreans with Kim giving up his nuclear programme though he acknowledged the process would likely take longer than a single meeting.
These include the central region, which is home to its foreign ministry, the US embassy and several hotels, and Sentosa Island in the south, where the summit is scheduled to take place.