The opposition boycotted the election, saying the violence threatened the lives of some of its supporters.
Mugabe returned home on Friday from an African Union summit in Egypt.
"I am the president of the Republic of Zimbabwe. and that is the reality everybody has to accept first and foremost if they want dialogue with us."
A draft Unite Nations Security Council text outlined an American plan for new sanctions against Mugabe's regime.
It requires countries to freeze the financial assets of Mugabe and 11 of his officials and to restrict their travel to within Zimbabwe's borders.
The draft also calls on Mugabe's government to immediately begin negotiating with the opposition to form a unity government and lift restrictions on humanitarian aid. (Www.hxen.com)
A latest statement issued by the European Union has called for new elections in Zimbabwe. It also called for renewed efforts from South African President Thabo Mbeki, who acts as Africa's mediator, to the issue.