"I think you've seen over the years how these two kinds of countries go on growing close together," Kirby said during a press briefing.
However, Kirby said he does not consider the closer ties between Russia and China an alliance, referring to the growing partnership as a "marriage of convenience" instead.
Russia and China are interested in serving as a counterweight to US and NATO influence, Kirby added.
The Biden administration official further stated that the White House does not see anything resulting from the Xi-Putin summit to suggest a timely ending of Russia's special military operation in Ukraine.
"I don't think the meeting today gives us great expectations that the war is going to end anytime soon," he told reporters.
The Tuesday briefing also saw the official refute past remarks that suggested arms would be given to Russia by China amid its ongoing special operation.
"We don't think that China's taking it off the table but they haven't moved in that direction," Kirby said. "We've seen no indication that they're about to or fixing to provide lethal weapons."
Kirby did also remark that ties between Russia and Iran appear to be strengthening.
Western countries significantly increased their economic and military support for Ukraine after Russia launched a special military operation there on February 24, 2022. The support well exceeds $100 billion and includes air defense and multiple rocket launching systems, tanks, self-propelled artillery, anti-aircraft guns, armored vehicles and various types of ammunition.
Russia has warned against further arms supplies that could mean direct involvement of the United States and NATO in the conflict.
Kirby's latest comments came amid Chinese President Xi Jinping's visit to Moscow this week on the invitation of Russian President Vladimir Putin, marking Xi's first trip abroad after his reelection for a third term in office earlier in March.
On Monday evening, Putin and Xi met informally for four-and-a-half-hours in the Kremlin. However, official talks began on Tuesday and Putin described them as highly productive to strengthening bilateral ties.