But the meeting would have come under the cloud of questions about Cohen's relationship with Moscow - and what he told the president while Trump was trying to win the White House. Kiev is hoping Trump will push Putin on the confrontation, which began Sunday when Russian Federation fired on Ukrainian ships trying to enter the Kerch Strait, a crucial waterway separating the Black and Azov seas.
In a subsequent tweet, Trump opened the door to another meeting once the recent incident with Ukraine is resolved: "I look forward to a meaningful Summit again as soon as this situation is resolved!"
But on Thursday, Trump tweeted that the meeting was off because of escalating clashes between Ukraine and Russian Federation near Crimea.
Relations between Washington and Moscow became the most strained since the end of the Cold War during the administration of President Obama who imposed sanctions for Russia's annexation of Crimea from Ukraine in 2014.
Following the incident, Ukraine's Navy said Russian Federation had "once again demonstrated its aggressive nature and complete neglect of the norms of global law".
There were further signs that Russian Federation was pressing ahead with its plans to fortify Crimea and turn it into what Kremlin-backed media have called a fortress. The Kremlin, however, said Thursday it could not confirm this news.
Kremlin spokesman Dmitry Peskov told reporters Thursday that the two leaders will start with one-on-one talks and then continue broader negotiations involving officials from both sides.
Meanwhile, Ukrainian President Petro Poroshenko asked North Atlantic Treaty Organisation countries to send naval ships to the Sea of Azov to aid his country and "provide security" amid tensions with Russian Federation.
Trump and Putin were supposed to meet in Argentina on the sidelines of the G20 summit, which gathers leaders from the world's 20 largest economies. Modeled on the President's Daily Briefing, or PDB, which the director of national intelligence prepares for the President nearly daily, my Presidential Weekly Briefing focuses on the topics and issues President Donald Trump needs to know to make informed decisions.
Speaking to reporters at the White House, he said that while China was interested in striking a deal, "I don't know if I want to do it" and "I like the deal we have now".
"For many, especially in the United States and perhaps among allies, such a meeting would signify that the USA approves of this action by Russia", Schultz explained.
FBN's Stuart Varney on President Trump's trip to the G-20 Summit.