One of the parties within the coalition government of President Robert Mugabe, the Movement for Democratic Change, installed Welshman Ncube in place of its previous leader, Arthur Mutambara who was demoted because of a change in his party's leadership structure.
Mutambara has declined to leave his post and Mugabe, who supports Mutambara, has declined to re-assign the minister, citing legal reasons, the Daily Nation reported Wednesday.
Ncube has accused Mugabe of tribal politics, saying last year he had no trouble complying with an opposition party's request to a Cabinet shuffle.
The party allegedly doesn't like Mugabe telling it what to do in a way that smacks of tribalism, the newspaper said.
"It is not the business of the president to use his powers as an appointing authority to resolve problems of a political party," George Charamba, the president's spokesman, said.
Charamba said Ncube's best option was to persuade Mutambara to agree to be re-deployed or leave the government.
Mutambara has not responded, the Daily Nation said.