President Obama said Tuesday that if the hack into the Democratic National Committee's email system ends up being tied to Russia, that fact wouldn't significantly impact his relationship with Russian President Vladimir Putin.

"I think we've already got a lot of differences with Russia on a whole lot of issues," he said during a press conference Tuesday with the prime minister of Singapore. "... If in fact Russia engaged in this activity, it is just one on a long list of issues that me and Mr. Putin talk about and one that I've got a real problem with."

Because Russia and the U.S. is at odds on so many serious foreign policy matters, his administration will continue to try to stay focused on "those areas where we still have a common interest," Obama said. He also declined to say whether he thinks Russia is to blame.

"It's not going to stop us from trying to find solutions to stop [Moscow's] bullying of Ukraine, and it's not going to stop us from trying to bring a transition to Syria to try to end the hardship there," Obama said.

He said it's "pretty standard" for the U.S. to have to balance competing issues when it deals with Russia.

If the FBI finds hard evidence that Russia was involved in the DNC email hack, he said there are "provisions in place" to impose "proportional penalties."

"But that requires us to really pin down and know what we're talking about," he said.

On Tuesday, one key Republican lawmaker condemned the Obama administration for trying to cooperate with Russia in Syria for another reason: coordination between Russia and Syria that has led them to "mercilessly" bomb hospitals, markets and aid warehouses in an attempt to force rebels in Aleppo to surrender.

Sen. John McCain, R-Ariz., called Obama's efforts to work with Russia "delusional," and referred to reports that the Assad regime has once again used chlorine gas against Syrian civilians. Those reports, he said, are "yet another reminder that the Assad regime has still not given up all of its chemical weapons, as international monitors have acknowledged."

"It is morally reprehensible that the Obama administration continues to pursue cooperation with Vladimir Putin in Syria at the same time Russian forces prop up the murderous Assad regime," he said in a statement. "The United States must not be complicit in allowing Assad to reconsolidate power and legitimizing Russia's expanded influence in the Middle East, which will only lead to more refugees, more instability and more terror.

"The Obama administration's policy in Syria has long been a failure. And its persistent delusions of Russia as a partner in Syria have been nothing short of embarrassing for our nation," he added.

If the administration does not change course now, McCain said, "it will be to the everlasting shame of this president and his administration."