The United States blames Mugabe for Zimbabwe's political deadlock, economic meltdown and humanitarian crisis, including a deadly cholera outbreak.
State Department spokesman Sean McCormack said Washington has been talking to Zimbabwe's powerful neighbor South Africa and other Security Council members about how to "start a process that will bring an end to the tragedy that is unfolding in Zimbabwe."
Countries with leverage should use it to press for change in Zimbabwe, McCormack said.
A senior US official, speaking on condition of anonymity, proposed Thursday that Zimbabwe's neighbors, particularly South Africa, close their borders with the country.
"You do not convene a UN Security Council meeting for a sovereign state without consulting that country," Information Minister Sikhanyiso Ndlovu was quoted as saying by the state-owned Herald newspaper.
"We are not a threat. If they insist, we will work hard to block it with the assistance of our friends," he said.