Washington(CNN) The Pentagon denied a recent claim by Russian defense minister Sergei Shoigu that he had invited US Secretary of Defense Jim Mattis for talks and that those invitations had been turned down.

"We have not received an invitation from Minister Shoigu requesting to meet with Secretary Mattis," Defense Department spokesman Eric Pahon told CNN.

On Wednesday, the Russian Embassy published an interview Shoigu gave to an Italian newspaper where he said that he had invited Mattis to meet "more than once."

"I have invited the Pentagon head to discuss current problematic global and regional security issues, including the war on terror, more than once. However, the Americans are not yet ready for such a dialogue. I am sure though that both the peoples of Russia and the US and the rest of the world are interested in that," the Russian defense chief said.

Summit ahead

The back and forth about high-level talks comes as President Donald Trump prepares to meet July 16 with Russian President Vladimir Putin in Helsinki, Finland.

"I hope we're going to be able to get along with Russia. I think that we probably will be able to," Trump said during a press conference Thursday following the NATO summit in Brussels, Belgium.

The Pentagon said that a better relationship between Russia and the US was contingent on Russia changing its behavior.

"The President has said he believes a better relationship with Russia would be good for both America and Russia, but the ball is in Russia's court," Pahon said.

Shoigu said that "the only working communication channel that exists" between the US and Russia involved the two countries' top military officers, Gen. Joseph Dunford, the Chairman of the Joint Chiefs of Staff, and his Russian counterpart Gen. Valery Gerasimov.

The two generals met in Helsinki last month and regularly speak on the phone to discuss the situation in Syria, where US and Russian forces operate in close proximity, as well as other issues according to statements issued by both the US and Russian governments.