President Trump's team has limited power to weaken Chinese support for North Korea, the State Department acknowledged Thursday.

"We can't force the Chinese to do anything, certainly," State Department spokeswoman Heather Nauert said during a press briefing Thursday.

The mild-mannered delivery nonetheless pointed to a serious issue: China's persistent willingness to shelter North Korea from a storm of economic sanctions demanded by western officials, even when they support them at the United Nations Security Council. Secretary of State Rex Tillerson has been working to overcome that recalcitrance for months, as North Korea has carried out a flurry of weapons program tests.

"If China is not going to comply with those UN sanctions, then it's appropriate for the United States to consider actions to compel them to comply," Tillerson said in January during his Senate Foreign Relations Committee confirmation hearing.

Trump's team stepped up those efforts in August, by imposing sanctions on an array of Russian and Chinese companies or individuals that have been doing illicit business with the North Koreans. And the Treasury Department put a spotlight on North Korean coal smuggling that runs through China and Russia.

But China and Russia rebuffed American and South Korean calls for an oil embargo that might bring dictator Kim Jong Un's regime to its knees. Instead, they backed a resolution that would only reduce oil exports to North Korea.

"I think it's clear that with respect to oil and a complete embargo of oil from the UN Security Council, that is going to be very difficult," Tillerson told reporters Thursday. "In effect, that is directed at China alone because China supplies essentially all of North Korea's oil."

Tillerson said that he is "hopeful" China will relent and cut North Korea's oil access, which Nauert emphasized as well. "This vote, the last vote, they've been taking some steps in the right direction," she said. "That would be another step that they could take."

Some senior lawmakers in both parties think the United States might have one viable path to force China to change course: country-wide sanctions.

"It's been a long, long time of waiting for China to comply with the sanctions we pass and frankly with the sanctions that the United Nations passed," House Foreign Affairs chairman Ed Royce said Tuesday. "This is where the discussion needs to go next, if there isn't full compliance with the sanctions that the UN have passed, because what's at risk is our national security."