Tayebwa made the remarks while opening the inaugural Parliamentary Week for the East African Community (EAC) at Parliament on Wednesday.
He called on regional parliaments to take a more active role in advancing the integration agenda by coordinating efforts, fast-tracking legislation and aligning policies across member states.
"Parliaments in the region must join efforts to coordinate and push for integration while fast-tracking laws and policies across the region," Tayebwa said.
The Deputy Speaker pledged Uganda's commitment to prioritising EAC matters in Parliament, saying reports and key issues concerning the regional bloc will continue to receive attention for debate and consideration.
He also emphasised the need to strengthen cooperation between the East African Legislative Assembly (EALA) and national parliaments to ensure a coordinated approach towards regional development.
Speaking at the same event, the Minister for Internal Affairs, Prof. Ephraim Kamuntu, said regional integration must focus on improving the lives of ordinary citizens.
"As national parliaments, legislators must work towards having an integration that is pro-people," Prof. Kamuntu said.
The Parliamentary Week is expected to feature discussions on EAC bills, committee reports and strategies aimed at deepening trade, free movement of people and political cooperation among member states.