Regarding Ukraine, the State Department also said "the sides will discuss the need to stop the violence in eastern Ukraine and resolve the conflict through the full implementation of the Minsk agreements".
The "foremost" aim of the de-escalation or safe zones is to protect peaceful civilians, but Assad said they also provide armed militants with an opening "to enter into a truce with the government".
A USA role in the successful creation of the safe zones and, eventually, in the resolution of the Syrian conflict is just as important as that of Russian Federation, and the fact that Moscow now is in charge of the situation in Syria should not preclude such role.
The US was not part of a deal by Damascus backers Russian Federation and Iran, and rebel supporter Turkey, signed Thursday in the Kazakh capital Astana on establishing safe zones in Syria.
"President Trump emphasized the need to work together to end the conflict in Syria, in particular, underscoring the need for Russia to rein in the Assad regime, Iran, and Iranian proxies", the White House said following the talks between the U.S. leader and the Russian foreign minister.
"The goal of both President Trump and President (Vladimir) Putin is to have concrete results which will be tangible and which will allow (us) to alleviate problems, including on the global agenda", Lavrov told journalists.
North Korea accuses US, South Korea of assassination attempt
North Korea has accused usa agents of masterminding an attempt to assassinate Kim Jong-un using a biological weapon. The U.S. has sent a warship to the region and installed a controversial anti-missile defence system in South Korea.
The US and Iran should show "compromise and flexibility" in helping secure the so-called deescalation zones proposed by Russian Federation to shore up a Syrian ceasefire, President Vladimir Putin's Middle East envoy, Mikhail Bogdanov, told reporters in Sochi on Thursday, Bloomberg reported.
Over the past six years, Moscow and Washington have sparred multiple times over the conflict in Syria, especially concerning Assad's fate.
The declaration contradicts Russian Federation, the main ally of Assad and principal author of the recently reached agreement, which had asserted there would be outside monitors.
The agreement calls for the creation of four "de-escalation zones" to shore up a ceasefire, ban flights and allow for humanitarian aid deliveries.
"We will look at the proposal, see if it can work", Pentagon chief Jim Mattis said Monday.
After the talks, Lavrov and Tillerson set off for Alaska and a meeting of the Arctic Council, a forum for cooperation on the environment, oil and mining, shipping, fisheries and tourism.