Russian Prime Minister Vladimir Putin (R) and U.S. Secretary of State Rex Tillerson look on at a signing ceremony in Sochi, Russia, Aug. 30, 2011, when Tillerson was the CEO of Exxon. Reuters

Secretary of State Rex Tillerson will not be meeting with Russian President Vladimir Putin during a scheduled to visit Moscow on Wednesday, a Kremlin spokesperson said Monday. Tillerson's trip comes amid growing tensions between the former Cold War adversaries over military conflict in Syria, and could signal a growing diplomatic rift between the two nations.

Read: Did Putin Help Trump Win? A Timeline Of Barack Obama's Relationship With Russia And The 'New Cold War'

Tillerson met with Putin several times when he was the CEO of oil giant Exxon, a role he relinquished in order to join the Trump administration. But after the U.S. attacked a Syrian airbase last week in response to a chemical gas attack ordered by Kremlin-backed President Bashar al-Assad, the diplomatic rift between the two countries has grown. Even Tillerson, who once received the "Order of Friendship" from Putin, will not have the opportunity to discuss the Syrian Civil War with the Russian leader.

"We have not announced any such meetings and right now there is no meeting with Tillerson in the president's diary," Putin spokesman Dmitry Peskov told reporters on a conference call Monday.

On Sunday, Tillerson said he was "hopeful" that the U.S. could work with Russia to "achieve areas of stabilization throughout Syria" and move toward a political solution to the six-year-old conflict. But he also had harsh words for Moscow.

"I think the real failure here has been Russia's failure to live up to its commitments under the chemical weapons agreements that were entered into in 2013, both by the Syrian government and by Russia, as the guarantor, to play the role in Syria of securing chemical weapons, destroying the chemical weapons and continuing to monitor that situation," Tillerson told "This Week" host George Stephanopoulos Sunday.

"But clearly, they've been incompetent, and perhaps they've just simply been out-maneuvered by the Syrians," Tillerson added.

While Tillerson was careful not to link Russia directly to the sarin gas attack that killed dozens of civilians last week, Republican Arizona Sen. John McCain said on Monday that Russia "knew about chemical weapons because they were operating exactly from the same base."

Putin met with former Secretary of State John Kerry several times to discuss the situation in Syria. Tillerson is scheduled to meet with Russian Foreign Minister Sergey Lavrov in Moscow. The two diplomats talked about the Syria situation by phone over the weekend, Russia's Ministry of Foreign Affairs said.