A joint statement issued early Wednesday morning said Bahrain, Egypt, Saudi Arabia and the United Arab Emirates would respond "in a timely manner." It did not elaborate.
Foreign ministers from the four countries are due to meet later Wednesday in Cairo.
The four countries early last month cut diplomatic ties to Qatar in large part over their allegations that it supports extremist groups. Qatar denies backing extremists.
They later issued a 13-point list of demands to Qatar to end the standoff. Qatar submitted a written response to mediator Kuwait on Monday.
Energy-rich Qatar hosts some 10,000 American troops at its sprawling al-Udeid Air Base.