In the past week, the Republican presidential nominee has been pilloried for his comments expressing openness to Russia's annexation of Crimea, has called on the Russian government to share emails it possibly hacked from Democratic nominee Hillary Clinton and drawn rebukes from critics who say he's soft on a traditional US adversary.

Former CIA Director Michael Hayden became the latest heavyweight in the George W. Bush administration to lash out at Trump when he criticized the candidate Monday night for making conflicting statements about his relationship with Russian President Vladimir Putin.

"I recognize that flexibility and creativity might actually be good selling used cars and selling real estate, but when you want to be the head of an international superpower, precision and consistency are really important," Hayden told CNN's Erin Burnett.

Hayden's comments come after Trump told ABC's "This Week" on Sunday that he has no relationship with Putin -- a remark that conflicted with Trump's long history of saying the opposite and embracing Putin's praise for his candidacy.

And a new CNN/ORC poll finds that most Americans see the Russian leader differently, with nearly 6-in-10 viewing the country as unfriendly, and about half saying they think the Russian government is attempting to influence the outcome of the US presidential election.

President Barack Obama, speaking Tuesday at a White House news conference, said Russia's potential hacking of the DNC wouldn't necessarily prompt a complete freeze in relations between the the country and the United States.

Noting the FBI was still investigating the hack, Obama said cybersecurity was just another dispute on a long list between himself and Putin.

"If, in fact, Russia engaged in this activity, it's just one on a long list of issues that me and Mr. Putin talk about," Obama said. "I don't think that it wildly swings what is a tough, difficult relationship that we have with Russia right now."

The debate over Trump's sympathy for Putin or take on world affairs is more than an esoteric squabble over foreign policy, experts said. By calling into question established structures and alliances that have held since World War II, Trump is unsettling allies and encouraging potential instability that inevitably draws the US to intervene.

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In his "This Week" appearance, Trump also echoed Moscow's claim that Crimeans welcomed Russia's annexation and seemed to suggest that Russia hadn't entered Ukraine at all, telling host George Stephanopolous, "The people of Crimea, from what I've heard, would rather be with Russia than where they were."

As for Putin's foray into Ukraine, Trump said, "He's not going into Ukraine, Okay, just so you understand. He's not going to go into Ukraine, all right?"

"Well, he's already there, isn't he?" Stephanopolous replied.

Sunday's exchange came in the wake of an alleged Russian computer hack of the Democratic National Committee -- seen as an unprecedented foreign effort to interfere in a modern US election -- and Trump's own call to Russia, which he later described as "sarcastic," to help find deleted emails sent by Clinton.

And the associations that his staffers have with Russian businesses and pro-Moscow interests complicates the campaign's efforts to push back against criticism on the subject and fend off questions about the Trump team's motivations.

Trump adviser Carter Page has extensive dealings with Gazprom, the Russian state-run energy company with strong ties to Putin and his inner circle. Trump campaign chairman Paul Manafort consulted for former Ukrainian President Victor Yanukovich, a key Putin ally, until his ouster in February 2014. In the chaotic aftermath, Russian-backed separatists seized the Crimea, a Ukrainian territory that Moscow later annexed.

In this context, Trump's comments expressing admiration for Putin are unsettling, said Evelyn Farkas, a former deputy assistant secretary of defense for Russia, Ukraine and Eurasia.

Trump's comments seemingly excusing Russia's invasion of Crimea throw into question his commitment to a system that has built a relatively peaceful and prosperous post-war order, said Farkas, now a senior fellow at the Atlantic Council. At a time when Russia as abrogated arms control treaties and its planes are buzzing US ships in the Baltic Sea, Trump has praised Putin as a canny leader who he respects.

Since the end of WWII, there has been an existing consensus among nations that borders should not be altered by force. Russia has deviated from that twice, in Georgia in 2008 and again in Ukraine.

"The international system is set up the way it is, and has provided relative peace and prosperity for decades," Farkas said. "To violate that is shocking and the bipartisan response has been 'this can't stand.' "

"If we accept the position that big states can ride roughshod over little states, that treaties are irrelevant and that we don't care whether we have solemn commitments to allies we are encouraging further attacks against our allies in Europe, Asia and the Middle East," said Stephen Blank, a senior fellow at the American Foreign Policy Council.

Whether the Crimean people welcomed Russia's invasion is irrelevant, said Blank, as "it was still a clear aggression of a country." And he noted that Trump's remarks have a potential ripple effect, providing an invitation for the estimated 25 million Russian minorities in post-Soviet states "to agitate for the dismemberment of their countries" and a return to the Russian fold.

"The international system is set up the way it is, and has provided relative peace and prosperity for decades," Farkas said. "To violate that is shocking and the bipartisan response has been 'this can't stand.' "

"The whole reason we have alliances like these is to deter countries like Russia from laying a finger on our allies. It's a way to prevent war, plain and simple," Farkas said.

Ukrainian Ambassador to the US Valeriy Chaly echoed Farkas' point Monday, telling CNN that while he didn't want to get involved in US election politics, Trump's comments concerned him.

"We count United States will be predictable, will have predictable leadership and predictable foreign policy," Chaly said.