The plans will now be put out for public consultation.
The proposals could see "large shops" in Belfast having their trading hours extended on up to 18 Sundays from March to September each year.
The step is possible by designating the city as a holiday resort under legislation from 1997.
A council paper states there is "a strong lobby" to review Sunday trading, currently permitted from 13:00-18:00.
It adds the move would boost the economy, benefit tourism and support the regeneration of the city centre.
Alliance councillor Kate Nicholl is backing the proposal.
She said: "I walked through Victoria Square one Sunday morning and came across a group of confused tourists who were keen to spend their money in our shops but were unable to.
"It is a scene that is repeated across the city every week."
Councillors have been told the move is permitted within the Shops (Sunday Trading) (Northern Ireland) Order 1997.
Some other Northern Ireland towns have already used it to extend Sunday trading, such as Portrush, Newry, Kilkeel and Ballycastle.
Plans to designate Belfast an official 'holiday resort' and to extend Sunday trading hours have passed their first stage at Belfast City Council.