If the conditions are upheld, Russia and the United States will work together to establish a Joint Implementation Center and carry out joint airstrikes against terrorist groups in the war-torn country, according to the deal.
"If, by Monday we have continued to see reduced violence and no humanitarian access there will be no Joint Implementation Center," Kirby told reporters on Friday.
Kirby noted that Secretary of State John Kerry had discussed aid delivery with UN Special Envoy for Syria Staffan de Mistura.
"We know that there are trucks that are waiting to go in, and the UN is supervising that process," Kirby said.
Earlier on Friday, the Russian Defense Ministry confirmed that Syrian government forces are ready to withdraw from Castello Road in Aleppo simultaneously with opposition groups to facilitate the delivery of aid.