"Right now we're not getting along with Russian Federation at all", Mr Trump said flatly during a White House news conference with Nato Secretary-General Jens Stoltenberg.
The remarks followed talks lasting two hours between Mr Tillerson and the Russian president Vladimir Putin. "We're going to see how that all works out".
Despite initial hopes in Moscow of better ties with the United States under Mr Trump, the two powers have descended into a furious war of words over the incident and a retaliatory USA missile strike against the forces of Moscow's ally Bashar al-Assad last week.
Tillerson said that Russian Federation could help Assad "recognize this reality".
Hopes may never have been high, especially after Russian Federation sounded a defiant note before Tillerson arrived in Moscow.
World's oldest person dies, aged 117
Brown, who is 117 years and 36 days old, took over from Italian Emma Morano who passed away today. "I separated from him in 1938". In addition to enjoying the single life, Morano didn't fuss with keeping a complicated diet to lengthen her time on earth.
Trump and others have indeed threatened similar action. Mr. Tillerson's suggestion that the Assad family dynasty was coming to an end in Syria was met with Mr. Lavrov's contention that hastily removing the Syrian leader would clear the way for the Islamic State group or al-Qaeda to seize control. Just two weeks ago, Russian Federation was in the driver's seat in Syria, as the lead military and diplomatic player in a peace process involving Turkey, Iran, the Kurds and rebel groups, all orchestrated by Putin. The most important part of this was that the United States was not getting in the way.
Russian Federation announced it was suspending use of the line last week after the US punished the Assad regime for the apparent use of chemical weapons by firing 59 cruise missiles at the airbase from which the attack originated.
Everything Putin did appeared aimed at minimizing the effect of Tillerson's visit.
More than 80 people were killed in what the US has described as a nerve gas attack that Assad's forces undoubtedly carried out. Denouncing a "very barbaric" attack, Trump ordered a strike that saw 59 Tomahawk cruise missiles slam into the airbase in central Syria from where Washington accused Assad's forces of launching the attack.
Assad said Syria's military had given up all its chemical weapons in 2013 after an agreement made at the time and that "even if we had them, we would not use them".
"We note that the official U.S. narrative was put forth very quickly, in the absence of an impartial and independent investigation, and in the absence of credible evidence", Murray said.
Hundred Gay Men In Chechnya Detained In Concentration Camps
Russian Federation has a bad track record on LGBTQIA issues but hasn't gone to the extremes alleged about Chechnya . The news of the round-ups comes on the heels of other reports of extreme violence and the detention of gay men.
Lavrov retorted: "This is obviously the subject where our views differ".
Lavrov called the evidence cited by Tillerson "hypothetical" and demanded that the United Nations investigate.
It was the eighth time during Syria's six-year-old civil war that Moscow has used its veto power on the Security Council to shield Assad's government.
"The world's two primary nuclear powers can not have this kind of relationship", Tillerson said Wednesday in Moscow after hours of meetings with Lavrov and Russian President Vladimir Putin.
Still, Mr Lavrov sought to put a positive spin on the talks with Mr Tillerson, saying they helped improve mutual understanding.
Russian Federation and the USA on Wednesday agreed to keep on fighting global terrorism and continue discussions on Syrian conflict settlement, despite turbulent bilateral relations and a string of pending disputes between the two countries.
ISIS lost most territory it held in Iraq
The United States and other Western countries have assisted with air support, intelligence and equipment, General Rasool said. ISIS has used hundreds of vehicle bombs along with drones rigged with explosives in Mosul.
Wednesday's meeting occurred amid the worst U.S. -Russia diplomatic relations since the end of the Cold War, more than a quarter-century ago.