Kim Jong Un and Donald Trump shook hands once again ahead of a private meeting with only their translators present.
The State Department is declining to release any additional information about the calls.
President Donald Trump made history Tuesday in Singapore as the first American president to meet face-to-face with a leader of North Korea since the Kim dynasty sprouted on the peninsula roughly seven decades ago.
But in an extraordinary media conference later, Mr Trump announced details not in the document.
Many lawmakers from both parties, while unready to declare the summit a diplomatic victory or defeat, remained skeptical the US could successfully negotiate a deal toward peace with Kim - but are letting the process play out.
The US side however reportedly believes that an immediate tangible outcome is unlikely following the meet.
The Korean Central News Agency (KCNA) reported on Wednesday: "Kim Jong-un invited Trump to visit Pyongyang at a convenient time and Trump invited Kim Jong-un to visit the US".
Trump and Kim met on Tuesday for a historic diplomatic summit.
Trump said the US will be monitoring the situation in North Korea to be sure that Kim is committed to dismantling his country's nuclear program. DPRK stands for the North's official name, the Democratic People's Republic of Korea.
Only hours before the White House announcement, US Secretary of State Mike Pompeo had seemed to lower expectations for the meeting, which Trump had earlier predicted could potentially yield an on-the-spot deal to end the Korean War.
President Donald Trump praised Kim Jong Un repeatedly following their nuclear summit Tuesday, a sharp reversal from when he publicly eviscerated the North Korea regime for human rights abuses past year.
The optimistic summit was a remarkable change in dynamics from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn labelled the President a "mentally deranged USA dotard".