Tillerson made these remarks after he met with his Russian counterpart Sergey Lavrov, on the sidelines of a G20 summit in Bonn, Germany on Thursday.
He also affirmed that the U.S. will stand up for its allies' interests if there is a difference between the two countries.
The meeting between the two leaders comes at a time when White House is presently embroiled in a controversy surrounding Russian links of former national security advisor Michael Flynn's that led to the his resignation.
"Where we do not see eye to eye, the United States will stand up for the interests and values of America and her allies. As we search for new common ground, we expect Russia to honor its commitment to the Minsk Agreements and work to deescalate the violence in the Ukraine." CNN quoted Tillerson as saying.
Under increasing pressure over his administration's relationship with Russia, US President Donald Trump on took a swipe at the previous Obama administration, suggesting it was "too soft" on Moscow over its annexation of Crimea.
Taking to Twitter, Trump commented that the Crimea peninsula was "taken" by Russia from Ukraine under the Obama administration.
"Crimea was TAKEN by Russia during the Obama Administration. Was Obama too soft on Russia?," he said.
Russia annexed Crimea, a territory in the former Soviet republic of Ukraine, in March 2014 following tensions with its neighbor.
Trump's Press Secretary Sean Spicer said Tuesday that the President has made it very clear that he expects the Russian government to deescalate violence in the Ukraine and return Crimea.
But on Wednesday morning, Russia's Foreign Ministry spokeswoman Maria Zakharova clearly stated that Russia would not return the territory.
"Crimea is part of the Russian Federation," she told reporters. Within hours, Trump tweeted, asking: "Was Obama too soft on Russia?"
During his campaign trail in July, Trump had said that the Ukraine crisis was "more of a Europe problem," and that the US should only step in on Crimea if European countries asked for help. (ANI)