The Russian and the US administrations were in contact after Trump called off his meeting with Putin on Thursday, but the two sides reached no agreement, Kremlin spokesman Dmitry Peskov was quoted by Russian media as saying.
The two presidents "reached an agreement to put an end to the implementation of new customs duties", said the minister of foreign Affairs of china Wang Yi, after a working dinner of more than two hours of the leaders and their advisers.
"As for top-level contacts, I am not against them".
Huckabee Sanders did not disclose the content of their conversation, but in a press conference later Saturday Putin revealed that Trump had questioned him about Russia's seizure of Ukrainian ships in the Black Sea.
Russia is resisting global calls to release three Ukrainian naval ships that its border patrols fired on and seized in the strait near Russian-annexed Crimea last weekend.
President Donald Trump will hold a make-or-break trade meeting with his Chinese counterpart at the G20 summit this week and also navigate a diplomatic minefield with Russia's president after unrest in Ukraine, the White House said Tuesday.
Vladimir Putin strode into the summit under a cloud, having drawn outrage from Europe over last week's incident in which his navy detained three Ukrainian ships and 24 sailors - causing Trump to abruptly cancel their scheduled meeting. "Hopefully, that will be resolved soon so that productive conversations can begin", Sanders told reporters in Buenos Aires.
Trump was meant to hold a one-on-one meeting with the Kremlin leader Friday, followed by an expanded session with their delegations.
Kremlin aide Yuri Ushakov said that Trump and Putin had a brief meeting on the sidelines of the summit Friday, reported Reuters.
"The current Ukrainian leadership is not interested in resolving this at all", Putin claimed.
Among other lies, Cohen said he told Congress that all discussions of the Moscow Trump Tower project ended by January 2016, when they had actually continued until June of that year. "Because when you have provocations, such hostilities like what just happened in the Black Sea...you can always use war to justify your economic failures".
Ukraine President Petro Poroshenko kept up the pressure from Kiev, saying Putin had refused to take his calls since the crisis started. The EU and North Atlantic Treaty Organisation called for de-escalation of the situation.
The summit itself, with leaders from France, Russia and Saudi Arabia among those attending, has been struggling to carve out any accord on fighting climate change while hot-button disputes such as Ukraine loom large.
Putin gave conflicting accounts of the Kerch incident.
Merkel said she had also discussed Syria with Putin, "especially. the Idlib region", where a fragile ceasefire has been negotiated between rebels and Syrian army forces backed by Moscow.
There are no plans, the White House says, for Trump to meet with Saudi Crown Prince Mohammed bin Salman, the de facto leader of the oil-rich Gulf kingdom.
Russian authorities said the Ukrainian ships breached the Russian border and conducted risky maneuvers in spite of orders of accompanying Russian vessels. "The ship's logs of the detained Ukrainian ships contain the task to penetrate the territorial waters of Russian Federation, and this is confirmed by the sailors' testimony".
He added: "Prior to that they said they were going to blow up our bridge so what do you expect our border guards to do?" - an apparent reference to Moscow's earlier claims that Ukrainian radicals planned to blow up a new bridge between Russian Federation and Crimea, which Russian Federation annexed in 2014. Fighting there has killed at least 10,000 people since 2014 but eased somewhat after a 2015 truce. Russian Federation has also supported separatists in Ukraine's east with clandestine dispatches of troops and weapons.