A seventh defendant, also from the rebel Justice and Equality Movement (JEM), was jailed for 10 years, lawyer Tahani Abdelrahim said
Abdelrahim said the sentences will be appealed.
The government announced two years ago that the seven were captured in West Darfur after a battle.
About 100 relatives of the accused attended the hearing at a downtown Khartoum court but everyone, including journalists, was ordered out for the sentencing by Judge Moutasim Tajalsir.
Abdelrahim said the accused stood and shouted in praise of JEM's late leader Khalil Ibrahim as they heard the verdict.
"Khalil is a martyr. We are following his path," she quoted them as saying.
Government forces said they killed Ibrahim in December. His brother took over as leader of the movement.
JEM spokesman Gibril Adam Bilal condemned the death sentences against its "prisoners of war" and called on the international community to ensure the punishment is not carried out.
One of those condemned to hang is from South Sudan.
More than 100 JEM rebels received the death penalty after the movement staged an unprecedented march to the outskirts of Khartoum's twin city Omdurman in 2008 before being repulsed.
President Omar al-Bashir later remitted many of the sentences.
Bashir and Defence Minister Abdelrahim Mohammed Hussein are wanted by the International Criminal Court for alleged crimes committed in Darfur.
In 2003, JEM and other rebels drawn from Darfur's non-Arab tribes rose up against the Arab-dominated Khartoum government. In response, the regime unleashed state-backed Janjaweed militia in a conflict that shocked the world and led to allegations of genocide.
Since then, much of the violence has degenerated into banditry.
The United Nations estimates that at least 300,000 people have died as a result of the Darfur conflict, while almost two million people remain displaced.
The Sudanese government puts the death toll at 10,000.
Last year, the government signed a peace deal in Doha with an alliance of Darfur rebel splinter factions, but JEM and other key rebels refused to sign.
Instead, they and insurgents fighting in South Kordofan and Blue Nile states formed the Sudanese Revolutionary Front to topple the regime they regard as unrepresentative of the country's political, ethnic and religious diversity.
