The TV announcement raised expectations the statement could be a sign that al-Bashir is relinquishing power or is being removed by the military after 30 years of rule.
Pan-Arab TV networks carried unconfirmed reports that al-Bashir had stepped down and that top ruling party officials were being arrested. The whereabouts of the autocratic leader, who is a pariah in many countries and is also wanted by the international war crimes tribunal for atrocities in Darfur, were not immediately known.
Organizers of the protests urged masses to converge and join an ongoing sit-in that has been underway in the capital, Khartoum, since the weekend.
They issued a statement vowing to remain in the streets until the "regime steps down completely and power is handed to a civilian transitional government."
Thousands of protesters, including women carrying their children, were seen making their way on Thursday toward the military headquarters, clapping and ululating, many flashing "V'' for victory. There were also unconfirmed reports that the airport in the Sudanese capital had been closed.
Ahead of the statement, Sudanese radio played military marches and patriotic music as the TV said there will be an "important statement from the armed forces after a while, wait for it."
The development followed deadly clashes between Sudanese security forces and protesters holding a large anti-government sit-in outside the military's headquarters Khartoum, which also include a presidential residence. There were several attempts to break up the sit-in, leaving 22 dead since Saturday.
All that raised the possibility that what was playing out in Khartoum on Thursday was a military takeover and removal of al-Bashir.