The high-profile Trump-Kim summit — the first meeting between sitting leaders of both countries — is set to take place Tuesday morning, but analysts have said they expect little direct impact on the markets.
Trump and Kim will likely discuss future bilateral ties, although no major breakthroughs are expected from the meeting.
U.S. stocks finished the last session in positive territory despite recent trade concerns after last week's tense G-7 summit, which Trump had attended before arriving in Singapore on Sunday. Trump had withdrawn his support to endorse the joint G-7 communique and criticized Canadian Prime Minister Justin Trudeau.
The Dow Jones industrial average finished higher by 0.02 percent, or 5.78 points, at 25,322.31, the S&P 500 added 0.11 percent to close at 2,782 and the Nasdaq composite ended the session up 0.19 percent at 7,659.93.
Trump continued to fan trade tensions in a series of tweets critical of traditional allies of the U.S. on Monday during Asia business hours.
Markets' positive tone came despite the uncertainty in anticipation of several key events expected this week.
"[The risk-on tone] may have been a function of low volumes ahead of the Federal Reserve and European Central Bank this week, as asset allocators are unlikely to make strategic investment decisions until those events and the Singapore summit are out of the way," ANZ analysts said in a morning note.
Ahead, the Fed begins its two-day policy meeting on Tuesday, with markets expecting a quarter-point interest rate hike announcement on Wednesday. The ECB and Bank of Japan hold meetings in the second half of the week.