Sudan's only involvement in the war in Yemen should be to help the warring parties reach a political solution to the crisis, the African country's new Prime Minister Abdalla Hamdok said as he pledged to withdraw Sudanese troops from the conflict.

Speaking at the Atlantic Council in Washington on Thursday, Hamdok said his government had "inherited" the military involvement in Yemen from longtime leader Omar al-Bashir, who was toppled in April after a popular uprising against his rule.

"The conflict in Yemen has no military solution, whether from us or from anywhere in the world," Hamdok said. "It has to be resolved through political means. We will help our brothers and sisters in Yemen and play our role with the rest to help them address this."

Sudanese soldiers and paramilitary fighters have been unofficially fighting alongside the Saudi-led coalition against Yemen's Houthi rebels.

Last month, a Houthi military spokesperson said more than 4,000 Sudanese fighters had been killed in the war in Yemen since 2015. At a news conference, the Houthi official displayed footage of dozens of soldiers he said were Sudanese prisoners of war.

On Thursday, Hamdok, who is leading a transitional government in a power-sharing agreement with the military, said "not many" Sudanese soldiers remained in Yemen, and vowed to "address" his country's involvement in the war "in the near future".

Asked whether he will be able to bring the Sudanese troops home, the prime minister said: "Absolutely."

Hamdok said his government is trying to move the country towards a brighter future after 30 years of autocratic rule under Bashir. He outlined a multi-faceted transitional plan that includes ending wars with rebel groups, revitalising the economy, ending corruption and upholding women's rights.

'Success story'

The prime minister received a warm reception from the mostly Sudanese audience at the Atlantic Council, with attendees - who greeted him with a lengthy standing ovation - interrupting his speech several times with rounds of applause.

His visit to Washington comes at a time of warming ties between the two countries. Earlier in the week, the State Department announced that the United States will be exchanging ambassadors with Sudan for the first time in 23 years.

American officials have lauded the Sudanese premier, voicing support for his transitional government.

"There is a success story in [the] making. Let us work together and make it a reality," Hamdok said.

He also addressed what he called "the elephant in the room", that is, Sudan's designation as a State Sponsor of Terrorism (SST) by the US.

Sudan remains on a blacklist - along with Syria, Iran and North Korea - despite the rapprochement between Washington and Khartoum since Bashir's fall.

He said Sudan's placement on the list is holding back many reforms, including the effort to tackle public debt and attract investment.

While Sudan had hosted al-Qaeda founder Osama bin Laden in the early 1990s, Hamdok said the Sudanese people will not tolerate terrorism today, and that they themselves had been victims of the terror of the previous government.

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The Sudanese government has a multi-billion dollar judgement against it in a US court for liability in al-Qaeda bombings of American embassies in Africa in 1998. Resolving those claims may be required to remove the country from the US terror list.

Hamdok said Sudanese diplomats are working with their American counterparts to solve these issues.

"We've progressed in this file very well," he said. Hamdok added that his government has been able to meet many of the conditions for removing Sudan from the list, including ensuring humanitarian access to conflict regions in the country and respect for human rights.

As for the legal claims, Hamdok said Sudan takes "corporate responsibility", without taking ownership of the deeds of Bashir's government.

"I think we are making progress in this," he said of the legal issues.