• Nagy would "urge parties to work towards creating an enabling environment" for talks between the two sides to resume.
• Four people were killed on the first day of the strike after security forces fired teargas and live ammunition.
The top US diplomat for Africa is going to Sudan this week amid the unrest there, the state department says.
Tibor Nagy, the US assistant secretary for Africa, will "call for a cessation of attacks against civilians".
Workers have staged a national strike, which began on Sunday, to pressurise the ruling military government to make way for civilian rule.
Four people were killed on the first day of the strike after security forces fired teargas and live ammunition.
The state department said Mr Nagy would "urge parties to work towards creating an enabling environment" for talks between the two sides to resume.
He will also discuss the situation with the Ethiopian Prime Minister, Abiy Ahmed, who has been trying to mediate between the military council and the opposition in Sudan, before later travelling to Mozambique and South Africa.
What happened during the strike?
Monday remained quiet in Khartoum, although some businesses started to reopen and a few buses were running.
Most shops, markets and banks in the capital, as well as in several other cities, remained closed on Monday as staff followed instructions from the Sudanese Professionals Association (SPA), the pro-democracy opposition, to not attend work.
The SPA called the strike after more than 100 peaceful protesters were killed by a paramilitary group, the Rapid Support Forces (RSF), on 3 June.
"The civil disobedience movement will begin Sunday and end only when a civilian government announces itself in power on state television," the SPA said in a statement.
"Disobedience is a peaceful act capable of bringing to its knees the most powerful weapons arsenal in the world."
Protesters have set up roadblocks across the capital. Social media users with access to a connection reported that the country's internet was blocked by the ruling military government.
In another development, three rebel leaders were deported from the city to South Sudan.
One of the three, Yasir Arman, had only returned to Sudan last month after years in exile after he was sentenced to death in absentia.