"Right now we're not getting along with Russian Federation at all", Trump said flatly during a White House news conference.
Tillerson met Putin in the Kremlin after talking to his Russian opposite number Sergei Lavrov for around three hours.
Peskov said in a conference call with reporters that Putin's meeting with Tillerson reflected the "understanding of the need to maintain a dialogue to search for solutions".
As Tillerson sat down for talks with Lavrov earlier on Wednesday, a senior Russian official assailed the "primitiveness and loutishness" of USA rhetoric, part of a volley of statements that appeared timed to maximise the awkwardness during the first visit by a member of Trump's Cabinet. "No", Trump said in the interview, which aired Wednesday in the U.S.
Western ambassadors blasted Russian Federation earlier Wednesday for continuing to support Syrian President Bashar al-Assad after his alleged use of sarin on a rebel-held area of his country.
It's the eighth time Russian Federation has vetoed a proposed Security Council resolution on Syria.
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He said "it would be a fantastic thing" if the two nations got along better but cautioned that "it may be just the opposite". "In general, primitiveness and loutishness are very characteristic of the current rhetoric coming out of Washington", Deputy Foreign Minister Sergei Ryabkov told Russia's state-owned RIA news agency.
But Lavrov said some progress had been made on Syria at the meeting and that a working group would be set up to examine the poor state of US-Russia ties.
Tillerson noted the low level of trust between the two countries. He added ominously, "The world's two foremost nuclear powers can not have this kind of relationship".
"It's hard to imagine Tillerson, now reportedly the front-runner for secretary of state under President-elect Donald Trump, saying something similar today, much less from a stage in Russia's second capital, Vladimir Putin's birthplace, and at a high-stakes, window-dressing government function". Moscow has strongly objected to a United States strike against the Syrian air base the West believes the sarin attack was launched from. Putin said that either gas belonging to the rebels was released when it was hit by a Syrian strike on a rebel arms dump, or the rebels faked the incident to discredit Assad.
Trump came to the presidency promising to seek closer ties with Russian Federation and greater cooperation fighting against their common enemy in Syria, Islamic State.
Russian Federation accuses Washington of faking the Assad responsibility in last week's chemical attack as a pretext, the way US officials trumped up a case for going to war in Iraq to destroy nonexistent weapons of mass destruction in 2003. But once Putin returned to the presidency, Obama's reset crumbled speedily, especially after Russia's 2014 annexation of Ukraine's Crimea region and support for pro-Russian separatists in eastern Ukraine.
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Before the MOAB attack, two alleged Indian recruits - Mohamed Mursheed and Mohammad Hafeezuddin -died in the past two months. The bomb struck a cave and tunnel system said to be that of an ISIS Khorasan stronghold on April 13 at 7:32 p.m. local time .
Ja'afari, the Syrian representative, repeated many arguments in his country's defense that he has stated over the six years of civil war.
"Mr. Tillerson's career is igniting a debate over the blending of business and politics - and whether that could tip the scales of in Russia's favor on major policy decisions like sanctions", the Times said.
The Putin meeting with Tillerson began shortly after 6 pm local time, the U.S. Embassy in Moscow said.
US Ambassador to the UN Nikki Haley told the council that "with its veto, Russia said no to accountability, Russia said no to cooperating with the UN investigation, Russia said no to helping keep peace in Syria, Russia chose to side with (Syrian President Bashar al-) Assad, even as rest of the world, even the Arab world, comes together to condemn the murderous regime". It is customary for USA secretaries of state to see Putin when they arrive in Moscow.
Still, Mr Tillerson sought to stress the positives from his meetings.
Safronkov charged that the United Kingdom and U.S. support terrorist groups seeking to remove the Assad regime.
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Until the chemical attack, the Trump administration had sought to step back from the U.S. position that Assad should leave power. "I think it's very bad for Russian Federation".