The tense back-and-forth over last week's deadly chemical attack in Syria has added to the strain.
He said Moscow was ready to resume a deal with Washington to avoid incidents in Syrian airspace as the two countries lead separate bombing campaigns. "The world's two foremost nuclear powers can not have this kind of relationship".
Wednesday's meeting brought no indication that the relationship would improve any time soon.
His top diplomat offered a similarly grim assessment from the other side of the globe after meeting with Russian President Vladimir Putin in Moscow.
The three foreign ministers insisted that the United States and its allies must respect Syria's sovereignty and territorial integrity and help the Syrian crisis to be resolved through holding national dialogue. Within 48 hours of the chemical attack, USA warships launched a cruise-missile strike against a Syrian airfield.
Trump said Tillerson had completed a successful meeting with Putin, where "things went pretty well". Tillerson said that while "there is a low level of trust between our countries..."
Trump and others have indeed threatened similar action.
Mr Tillerson's visit to Moscow comes amid mounting tensions.
For Russia, she said, "getting serious about peace starts by fulfilling its commitment to get chemical weapons out of Syria". After all, Putin and Trump are buddies. Any expectations of an easy rapport have crashed into reality amid the nasty back-and-forth over Syria and ongoing US investigations into Russia's activity connected to the USA presidential election. It can be assumed, however, that Putin will not support any outcome that results in a Syrian government that is not friendly with Moscow.
US and Russian leaders have exchanged sharp words since USA military missiles struck Russia's ally, Syria, in response to its regime's use of chemical weapons on civilians less than a week ago. Until the chemical attack, the Trump administration had sought to step back from the US position that Assad should leave power.
"We are not going into Syria", he said, adding that he had felt the need to act after the Syrian government violated an agreement made with the Obama administration to remove its chemical weapons.
Tillerson denied knowledge that Russian Federation was somehow involved in the chemical attack, but said: "What we do know...is that the attack was planned [and] carried out by the regime forces of Bashar al-Assad".
Lavrov had a ready retort: "This is obviously the subject where our views differ".
The draft would have demanded that the Syrian government provide flight plans, flight logs and other information on its military operations on April 4, hand over the names of commanders of any aircraft and provide access to air bases to United Nations investigators.
On Wednesday, Russia vetoed a US, UK, France-proposed resolution on the investigation into the Idlib chemical attack.
The two also announced new measures meant to prevent things from getting worse: Moscow and Washington will set up a working group created to improve their relationship, Lavrov said, and Putin has agreed to restore a bilateral U.S. -Russia safety agreement over Syrian skies, which Moscow announced it had suspended in the wake of the missile strike.
Zarif later sat down with for talks with the Russian foreign minister to discuss closer Tehran-Moscow cooperation in regional and global issues as well as the fight against terrorism.
It doesn't matter if this shift is due to the congressional investigation into allegations that certain close aides of Trump developed ties with Russian Federation in the runup to the USA elections.
The secretary of state and national-security advisor are both missing a key point: Russian Federation is acting in ways consistent with how it sees its national-security interests in the region.
Lavrov seemed to delight in recalling US attempts to oust dictators in Sudan and Libya. Washington doesn't do itself any favors by mocking and deriding the world's second-most-powerful military power, which, if engaged properly, has the ability to help with this primary security goal. "These are the same people that said Saddam Hussein had weapons of mass destruction", he said.
"Right now we're not getting along with Russian Federation at all", Trump said flatly during a White House news conference with NATO Secretary-General Jens Soltenberg.
Trump himself seemed to deliver the coup de grâce.
US Secretary of State Rex Tillerson is to urge Russian Federation to stop supporting Syrian President Bashar al-Assad after last week's chemical weapons attack.
That sounded like something both Lavrov and Tillerson agreed with.