Police in the California city shot dead a driver after the vehicle crashed Monday into the consulate's visa office.
The State Department said it was in touch with its counterparts in China, which had said it made "solemn representations" to Washington and urged "serious punishment" over the attack.
"We are committed to addressing this issue, consistent with our obligations under the Vienna Conventions relating to safety and security of diplomatic facilities and personnel," a State Department spokesperson said.
"We condemn all violence perpetrated against foreign diplomatic staff working in the United States."
San Francisco is home to a large number of ethnic Chinese residents, many of them critical of Beijing.
Violence against diplomatic missions is rare in the United States, but the Cuban embassy in Washington has been attacked twice in recent years, most recently by a person who last month threw two Molotov cocktails.
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