'We should be friends with every country in the world,' former Sen. George Mitchell says

Sen. Mitchell: US isn't problem with US-Russia relations

The United States should maintain its relationships with countries around the world rather than tearing up key agreements when the new administration steps in, former United States Sen. George Mitchell told CNBC on Monday.

Mitchell's main concern was President-elect Donald Trump's relatively soft stance on U.S.-Russia relations, which the former Democratic majority leader said were worrying considering Russia's violation of international law in the Ukraine.

"We should be friends with every country in the world and we want to be. But if you begin with the premise that the problem in the United States-Russia relationship is the United States, I think that's the wrong premise," Mitchell said on CNBC's "Squawk Box."

The former senator said that U.S.-imposed sanctions should be upheld while key points of contention with Russia come to light, such as the war in Syria and, more recently, Russia's alleged involvement in influencing U.S. election results.

"We should work with them where we can, but it is clear that in the Syria discussions they've been dragging their feet, enabling [Syrian President Bashar al-Assad] to regain control of Aleppo," Mitchell said.

Mitchell said that Trump's rumored pick for secretary of State, Exxon Mobil CEO Rex Tillerson, if appointed, should shift his position on Russia in the interest of the United States.

"I hope very much that if he is nominated that he will very quickly say ... that 'I opposed sanctions on Russia as a private citizen and as part of a large company that was adversely affected by those sanctions, but as secretary of State, I now represent all the people of America and I believe the sanctions program is the appropriate response,'" the former senator contended.

Mitchell also expressed concern about the Iran nuclear deal, which was passed by President Barack Obama in January to limit Iran's capacity to build a nuclear weapon.

"[The] president-elect has said he's going to tear up the Iran agreement. I hope he doesn't. I think that would be a profound error. It will contribute to upheaval in the region, and possibly involve the United States militarily even more deeply," Mitchell said.

On the topic of China and Trump's recent phone call with the democratically elected president of Taiwan, Mitchell said that there was a risk of "rupturing relations with China, with whom we have a very close economic relationship."

The former senator said that even if Trump feels the relationship is one-sided, there are more diplomatic ways to settle the two nations' differences.

"You don't have to tear up the relationship to address what grievances we have," Mitchell said.