Zimbabwe's new prime minister, Morgan Tsvangirai, has called on the world "to get over" President Robert Mugabe and stop seeing him as the principal problem facing his country.

Speaking to the Guardian shortly before ministers in the new powersharing government were due to be sworn in today, Tsvangirai said that his most immediate challenges – from finding the money to pay government workers and prising political detainees from prison, to purging the system of some of its worst crooks– now have little to do with the man who has ruled Zimbabwe since independence 29 years ago.

"Unfortunately people are preoccupied with Mugabe as a person. They need to get over it. This has gone beyond Mugabe. People need to stop talking about him as the only issue. Mugabe is part of the problem but he is also part of the solution. He is not the obstacle we are now facing," he said.

But hours later, Tsvangirai received a sharp reminder of another more sinister challenge his administration faces as one of his new ministers, Roy Bennett, was arrested today. The Movement for Democratic Change said Bennett, a former white farmer who is a particularly hated figure within Mugabe's Zanu-PF, was "abducted" by the police law and order unit.

The detention, along with the continued imprisonment of dozens of opposition supporters who have been held for months and tortured, reflects deep divisions within the upper echelons of Mugabe's power structure, with some of the military chiefs apparently attempting to sabotage the powersharing agreement that brought Tsvangirai into government.

The MDC believes that if it can establish itself as a partner in government, pay civil servants and bring in foreign aid, power will bleed from Mugabe and Zanu-PF to Tsvangirai.

But the coming days will be difficult as hardliners, such as the armed forces chief, Constantine Chiwenga, the police chief, Augustine Chihuri, and other senior security officials who said they would never recognise Tsvangirai's authority, keep up attempts to undermine the new political setup.

The new prime minister won immediate support from government workers after his inauguration on Wednesday by promising that civil servants, the police and soldiers – struggling along on salaries in nearly worthless Zimbabwe dollars – will be paid in hard currency at the end of the month.

But there were immediate questions about where the money to pay them is coming from, given the state's coffers are nearly empty and foreign governments have said they want to see if Tsvangirai is really in charge before they start handing over a £1.2bn aid package.

Tsvangirai needs to find about $100m by the end of the month to pay 236,000 civil servants, teachers and health workers, as well as the police and military, in foreign currency. Some of his party colleagues had urged him not to make such a specific commitment at his inauguration. But the new prime minister told them that there was no hope of beginning to rebuild Zimbabwe without getting government employees back to work.

"It was not something lightly considered. It's not something you just say. We will meet the commitments. I can assure you we will find the funds," he said.

Eddie Cross, nominated to be the MDC's new state enterprises minister, said the government already had a commitment of $50m from foreign donors, although he did not name them.

Money is the key to reviving Zimbabwe's economy, but Britain and other donors have laid down several standards by which the new administration will be judged, before the money is released. These include a return to the rule of law, the freeing of political detainees and the lifting of draconian restrictions on the independent press.

"People have set benchmarks," said Tsvangirai. "We have to earn the confidence of the international community. Their scepticism is justified. This is 29 years of one-man rule. But I'm quite certain if we start moving on the benchmarks, that will be the basis for incremental support. It's a process of engagement."

An early marker will be the fate of the central bank governor, Gideon Gono, who has overseen world-record inflation running above 10 sextillion percent and the eradication of the national currency, as he did the electronic equivalent of furiously printing money by adding strings of zeros to government bank accounts. He also facilitated the plunder of Zimbabwe's coffers by its ruling elite.

Western governments want him out. So do most Zimbabweans, but he has clung to office in part because he has a hold over other Zanu-PF leaders, because he knows who stole what.

Tsvangirai acknowledges that getting rid of Gono and the attorney general, Johannes Tomana, who has abused the law to lock up Mugabe's opponents, will be seen by foreigners and Zimbabweans as an early test of his power.

"We are dealing with that issue of Gono. The government has to deal with it because I appreciate that people have no confidence in our central bank governor and our attorney general. It is an issue that was addressed in the [South Africa-brokered regional] negotiations. It will be dealt with," he said.

Asked how, he said: "We recognise that it will be hard to win the donors' confidence if the central bank governor is still there. I cannot say more right now but it will be dealt with."

Another early test is the fate of 30 political detainees who have been held for months and brutally tortured. Tsvangirai sought to dampen accusations that he is not doing enough for them, in part because he abandoned a pledge not to be sworn in until they were free, by visiting Chikurubi maximum security prison yesterday and demanding to see the political prisoners.

He succeeded in getting three of them moved to a private clinic for treatment, including Jestina Mukoko, who is reported to be ill. But prison authorities removed Mukoko from the hospital a few hours later and returned her to jail.

Tsvangirai acknowledges that their continued detention is seen by many as a test of whether he wields sufficient power to overcome the hardliners.

"I do agree that it's a question of credibility," he said. "I went to the prison and talked with them and said it is taking longer than we anticipated but we are dealing with it."

Asked why it is taking longer than anticipated, he said:"The problem is not Mugabe. It lies elsewhere. It is others. We need to overcome that," he said, declining to name names.

Tsvangirai said that while the dissent by the old regime's hardliners was of concern, he did not believe they would be able to retain power or carry out a coup.

"The region won't accept it. The world won't accept it. They can't get away with it," he said "We know there are people who are disgruntled. We know the agreement does not have support from all parties. The leadership challenge for us is to negotiate away these areas of disgruntlement. We can do that and we are going to begin by getting people back to work."