"We hope the parties concerned can engage in serious dialogue to find a proper solution," Yang said, adding that "China as a responsible country will also play a constructive role in this process."
Rice had been hoping to persuade China – a leading ally and trading partner of Zimbabwe – to join US efforts to step up pressure on Robert Mugabe, who was sworn in for a controversial sixth term on Sunday as Zimbabwe's president.
On Saturday George Bush, the US president, said he had ordered officials to come up with ways to further punish Mugabe and his allies.
That could mean steps against his government as well as additional restrictions on the travel and financial activities of Mugabe supporters.
But Bush also wants the security council to impose an arms embargo on Zimbabwe as well as travel bans on Zimbabwe government officials.
Lashing out at the Zimbabwean leader, Bush said Mugabe headed an "illegitimate government" that had retained power only through a "sham election that ignored the will of the people of Zimbabwe."
Rice has said the US is looking to puts its plans for action against Zimbabwe before the security council later this week.
The United States holds the council's rotating presidency until July 1, but appears to face an uphill battle in winning over several key members to agree to any penalties.
In addition to China, both Russia, also a permanent veto-wielding council member, and South Africa, an elected council member, have opposed action saying the situation is an internal matter for Zimbabwe that does not warrant council action.
Speaking after Sunday's talks in Beijing, Rice said the US would continue to pursue the matter.
"Frankly, it makes sense to deny the government of Zimbabwe the means to use violence against its own people," she said.
There is currently no international arms embargo against Zimbabwe and China is one of the country's main suppliers of weapons and ammunition.
Earlier this year a Chinese freighter carrying guns and other weapons bound for Zimbabwe was refused permission to dock at several African ports, partly at the urging of the US.
Commenting on the issue, Yang said the shipment had been returned "at the request of the receiving party".