CNN — When President Joe Biden meets Chinese President Xi Jinping on Wednesday for a rare, high-stakes summit, two major wars – the Ukraine-Russia conflict, now deep into its second year, and the Israel-Hamas war that has entered its second deadly month – will serve as the backdrop amid extraordinary global tumult.

Members of the American and Chinese delegations plan to discuss both conflicts in their intensive, multi-hour meetings in the San Francisco Bay Area, according to senior administration officials, and Biden and his national security advisers will seek to convince their Chinese counterparts it is in Beijing’s interests to use its leverage with Russia and Iran to keep both wars contained.

The global unrest ratchets up the stakes of Biden’s sit-down with Xi, their first face-to-face meeting in a year. As Biden confronts two presidency-defining conflicts in Ukraine and Israel, he is eager to improve ties with Beijing and prevent another crisis from exploding on his watch. The US has sought to manage expectations for the talks, pointing to the restoration of military communication and an agreement to curb narcotics trafficking as top objectives.

Even as he applies pressure on Xi, Biden’s own ability to shape the wars in the Middle East and Europe is being tested, as Israel continues its assault on Gaza’s civilian infrastructure and as Ukraine struggles to regain territory following Russia’s invasion 20 months ago. His staunch support and billions of dollars in military assistance from the United States haven’t necessarily led to outcomes US officials had hoped for.

Speaking a day before leaving for San Francisco for his meeting with Xi and a summit of Pacific Rim leaders, Biden acknowledged daylight between the US and Israel over its war strategy, saying hospitals “must be protected” and that his “hope and expectation is that there will be less intrusive action.”

In California, the president plans to personally press Xi to use China’s rare alliance with Iran to help deliver what has been an unanimous warning from western world:Don’t add fuel to the fire.

“The president will underscore our desire for China to make clear in its burgeoning relationship … with Iran that it is essential that Iran not seek to escalate or spread violence in the Middle East,” a senior administration official said.

Echoing what Biden and his top officials have said repeatedly in recent weeks, the president plans to also make clear to Xi that “if Iran undertakes provocative actions anywhere that the United States is prepared to respond and respond promptly,” the official added.

China’s influence has grown in Iran as the two countries have found common cause in mutual antipathy toward the United States. China purchases large amounts of Iranian oil and has made investments in the country, deepening a strategic partnership whose animating feature is opposition to American interests.

A senior Chinese diplomat visited Iran over the weekend, and reiterated Beijing’s calls for an end to the fighting and condemnation of civilian deaths.

When Chinese Foreign Minister Wang Yi visited Washington last month in preparation for this week’s Biden-Xi meeting, senior US officials raised the Middle East issue, pressing China to adopt a “constructive” approach to the conflict.

“China obviously has relations in the region,” a senior administration official said. “We think it should be using those connections to call for calm on all sides.”

China has frustrated Israel by not taking a harder line against Hamas, and for its critical stance toward the operation in Gaza. Wang said in a meeting with Saudi Arabia’s foreign minister that the military campaign went “beyond the scope of self-defense.”

For Biden and his aides preparing for Wednesday’s meeting with Xi, their chief objective won’t necessarily be to convince China to support Israel’s efforts, but to convince Iran not to escalate any further.

“President Biden will make the point to President Xi that Iran acting in an escalatory, destabilizing way that undermines stability across the broader Middle East is not in the interests” of China or “any other responsible country,” US national security adviser Jake Sullivan said Monday at the White House.

How successful Biden is on that front won’t be known at the summit’s conclusion. And American officials have acknowledged that it is unlikely China will stop purchasing sanctioned Iranian oil – much like it continues to purchase energy from Russia, despite the raft of western sanctions applied at the start of the Ukraine war.

Still, US officials believe there might be a limited role Beijing can play in the Ukraine war, notwithstanding China’s deep economic alliance with Russia.

Since the earliest stages of the Ukraine war, Biden has sought to convince Xi to withhold support for his ally in Moscow, President Vladimir Putin. Like Iran, Russia shares China’s aims of reshaping what they see as an American-led world order hostile to their aims. Xi and Putin have said their relationship has “no limits.”

China has said it remains “impartial” in the Ukraine conflict and has suggested it could play a peacemaking role, an offer Washington has been skeptical of.

The Biden administration has grown increasingly concerned about the strengthening of ties between North Korea and Russia, particularly as the hermit nation has appeared eager to provide Russia with military supplies.

To that end, in Wednesday’s meetings, US officials intend to “underscore our continuing concerns around those provocations to China, who continues to be a substantial patron of North Korea.”