Moscow and Washington are increasingly at odds over President Trump's decision to authorize the missile strikes in Syria last week. Since last Thursday's cruise missile strike, Tillerson and other US officials appear to have reverted to the past administration's rhetoric of insisting that Assad is on the way out, without outlining any strategy for making that happen.
But divisions arose as UK Foreign Secretary Boris Johnson proposed sanctions against Syrian and Russian military figures over the chemical attack. On Friday, Russia's Defense Ministry said in a statement only 23 of the U.S. missiles made it to the airbase, blowing up just six MiG-23 planes.
He said the message for Russian Federation was: "That's enough now".
While briefing reporters Monday, Central Command spokesman Thomas said the number of U.S. strikes against Islamic State militants in the region has been reduced as U.S. Lt. Gen. Stephen Townsend, the ground commander for coalition forces in Iraq and Syria, repositions forces to assure force protection for his troops. Then the North Atlantic Treaty Organization expanded eastward, the USA bombed Russia's ally Yugoslavia and relations got sticky.
But what of all the others actors in the many-sided Syrian conflict?
"Congress needs to work with the president to try and deal with this long-term strategy, lack of strategy, really, in Syria", he said.
And he says there is no Russian interest in allowing the current disagreements over Syria to lead to a broader confrontation.
Johnson denied he had suffered a defeat, saying there was support for sanctions if further evidence of the chemical attack were gathered.
Over the weekend, Alfano said that Europe's broad support for the US military strikes had contributed to a "renewed harmony" between the United States and its partners as the G-7 foreign ministers prepared to meet for the first time since Donald Trump took office in January.
Bashar Assad's days as president of Syria are numbered, Prime Minister Justin Trudeau suggested Monday as more hostile talk from worldwide powers continued to amplify the threat of a military escalation in the Middle East.
Foreign ministers from the Group of Seven industrialized nations met Monday to try to forge a common response to the deadly chemical attack in Syria, with new sanctions against Russian backers of President Bashar Assad one of the options on the table.
President Trump's son Eric said that the USA would not be "pushed around" by Mr Putin, the Daily Telegraph reports. This includes the arrest of Russians in third countries by USA forces, violation of that northern country of the rights of adopted Russian children or the creation of artificial obstacles for the work legally established of our diplomats, it stresses.
On Monday Tillerson raised fresh expectations for aggressive US action - and not only in Syria - as he visited the site of a Second World War Nazi massacre in central Italy, saying the USA would hold to account "all who commit crimes against the innocents anywhere in the world".
It is also taking place amid an ongoing terror threat that was underscored by the Palm Sunday bombing of Coptic churches in Egypt claimed by the Islamic State group, and another truck attack on European soil, this time in Stockholm, on Friday.
Italian Foreign Minister Angelino Alfano, the host of a two-day G-7 meeting in the ancient Tuscan town of Lucca, called a parallel gathering for Tuesday with counterparts from Turkey, the United Arab Emirates, Saudi Arabia, Jordan and Qatar, a ministry official said.
In a joint Russian-Iranian statement, the two countries stressed that the United States strike on Syria had crossed red lines.
Western countries have been calling for Assad to leave power since 2011, the start of a civil war that has killed at least 400,000 people and created the world's worst refugee crisis.
"It is clear to all of us that the reign of the Assad family is coming to an end", he said. "But the question of how that ends and the transition itself could be very important in our view to the durability, the stability inside of a unified Syria".
"That's why we are not presupposing how that occurs", Tillerson added.
Lavrov and Tillerson are expected to discuss bilateral relations plus Syria, Ukraine, Libya, Afghanistan and North Korea.