A party spokeswoman said on Wednesday that the decision of the new government was agreed on by two only parties without an election.
"We are not interested in participating in this new government until there are elections," said Mariam al-Mahdi.
"Our absolute judge is the people of Sudan. ... We are very
determined to participate in and are preparing for the next
The Umma party is led by former prime minister Sadiq al-Mahdi, Sudan's last democratically elected leader and the father of Mariam al-Mahdi.
The party has a wide support base in the north and west of Africa's largest country.
Under a peace deal signed in January between the former southern rebel Sudan People's Liberation Army and the ruling National Congress Party, power and wealth will be shared with the outlying regions of the country, a new government of national unity will be formed and elections will be held within three years.
But Mariam al-Mahdi said the government due to be formed on July 9 was not a government of national unity but one exclusive to the two parties to the peace deal.