But Russia's brutal invasion of Ukraine has made that vexing move even more complicated. China's government has vacillated between full embrace and more measured responses as Russian President Vladimir Putin prosecutes his war, making the decisions for Biden far more layered.

"It's difficult. It's expensive," Kurt Campbell, the co-ordinator for Indo-Pacific Affairs on the White House National Security Council, said during a recent forum regarding maintaining a high-level US focus in two regions.

"But it's also essential, and I believe we're entering a period where that's what will be required of the United States and of this generation of Americans."

That leaves the Biden administration needing to focus on the East and West at the same time, balancing not simply economic imperatives but military ones as well.

The President has been deeply invested in rallying NATO and Western allies to respond to Russia with crippling sanctions, supplying an overmatched Ukraine military with $US2 billion in military assistance - including $US800 million in new aid announced Wednesday - and addressing a growing humanitarian crisis.

Eastern-flank NATO allies, including Estonia, Latvia, Lithuania, Poland and Romania, have made it clear to the Biden administration that they want the US to increase its military presence in the region and do more to address the worst humanitarian crisis in Europe since World War II. More than 3 million Ukrainian refugees have fled their country in recent weeks.

Though the war in Ukraine has dominated Biden's focus of late, White House officials insist they haven't lost sight of China - and are watching intently to see how Xi Jinping decides to play his hand.

In recent months, Biden has announced the sale of nuclear submarines to Australia and raised the profile of the Indo-Pacific security dialogue known as the Quad (Australia, India, Japan and the United States). He's also called out China for military provocations against Taiwan, human-rights abuses against ethnic minorities, and efforts to squelch pro-democracy advocates in Hong Kong.

Biden's national security team was somewhat surprised that America's Pacific partners - Australia, Japan, New Zealand, Singapore and South Korea - moved so quickly to hit Russia with sanctions following the invasion, according to a US official familiar with the administration's thinking.

The official, who spoke on condition of anonymity to talk about private discussions, says there was a recognition among Pacific allies that Beijing is watching how the world responds to Russia, as China calculates how aggressive it can be with its smaller neighbours in the region. In backing sanctions, the Pacific nations were trying to send a message to Xi as well as Putin, the official adds.

From the first days of his presidency, Biden has said the aims of his China policy are to find ways to co-operate with Beijing on issues of mutual interest - such as stopping North Korea from developing nuclear weapons, and coaxing Tehran to return to the Iran nuclear deal with the US, China, Russia and other world powers - and to avoid confrontation.

To that end, White House national security adviser Jake Sullivan and senior Chinese foreign policy adviser Yang Jiechi met earlier this week for an intense, seven-hour talk about the Russian invasion and other issues. They spent part of their time together discussing North Korea's recent intercontinental missile tests.

Still, Beijing's approach to the Russian invasion is causing Washington concern. The White House has made clear to Beijing that throwing a lifeline to Russia's collapsing economy or assisting its bruised military would be hazardous to a country that sees itself as the next great world power. The White House has not publicly specified what actions it would take should China assist Russia.

"We don't need China to be with us. We just need them not to be against us," says Frank Jannuzzi, president of the Maureen and Mike Mansfield Foundation, which focuses on US-Asia relations.

Xi and Putin met in early February, weeks before the invasion, with the Russian leader traveling to Beijing for the start of the Winter Olympics. During Putin's visit, the two leaders issued a 5000-word statement declaring limitless "friendship".

In the days after Putin ordered the invasion, Xi's government tried to distance itself from Russia's offensive but avoided criticising Moscow. The government has offered to act as mediator and denounced trade and financial sanctions against Russia.

At other moments, Beijing's actions have been provocative.

Last week, Chinese Foreign Ministry spokesman Zhao Lijian echoed unsubstantiated Russian claims that there were 26 bio-labs and related facilities in Ukraine of "which the US Department of Defense has absolute control". The United Nations has said it has received no information backing up such accusations.

White House press secretary Jen Psaki took to Twitter to charge that the Russian claim was "preposterous" and could be part of an attempt by Russia to lay the groundwork for its own use of such weapons of mass destruction against Ukraine. She also blamed China for having "seemingly endorsed this propaganda".

Xi's government has also sought to use the conflict to accentuate Chinese ascendancy and the decline of the West.

But China has its own internal troubles, including a major economic slowdown, difficulties that sanctions against Russia could make worse.

"The Ukraine war has proceeded in ways China did not expect, and the war is not conducive to China's rise or development," says Xiong Zhiyong, professor of international relations at China Foreign Affairs University.

Still, concerns that China could come to Russia's aid have only deepened at the White House in recent days.

On the same day of the Sullivan-Yang meeting, the US informed Asian and European allies that American intelligence had determined China had signalled to Russia that it would be willing to provide both military support for the campaign in Ukraine and financial backing to help stave off the impact of severe sanctions imposed by the West.

White House officials said Sullivan had made it clear there would be "severe" consequences should China assist Russia.

Ryan Hass, who served as China, Taiwan and Mongolia director at the NSC during the Obama administration, says Beijing faces a "momentous decision" on whether to aid Russia.

If Xi decides to do that, "it's hard for me to see how the path remains open for China to maintain non-hostile relations with the United States and others in the West," Hass says.

At the White House, Psaki has said any country doing business with Russia should "think about where you want to stand when the history books are written on this moment in time".