John Kerry says the bombings underscore the urgency of unity in the fight against so-called Islamic State.
Police in Brussels arrested 6 people in overnight raids in the city.
The 6 arrests were made in the North East suburb of Schaerbeek in the same district the 3 confirmed suspects from Tuesday's attacks emerged.
Over the last few days, Belgian authorities having been raiding several homes in search of evidence and on Wednesday they found chemicals required for the home-made suicide bombs used by both the Brussels and Paris attackers, also in an apartment in Schaerbeek.
Meanwhile in Paris the interior minister, Bernard Cazeneuve confirmed that police arrested a French national saying only that he was thought to be at an advanced stage of orchestrating a terror plot.