I am looking for recommendations for apartment-style hotel in Rome and Venice. We stayed at Fraser Suites Le Claridge Champs-Elysιes in Paris and it worked out very well with 3 bedrooms, 3 bathrooms, kitchen and seating area. Does a similar-type property exist in Rome and Venice? I do not want an Air B&B, etc.

Just google 'Aparthotel' and/or 'Apartment Hotel' in both cities -

I go to booking.com, enter all dates and how many people, 2+ bathrooms depending on people and it will give you list and amount. I then go book direct with the place. We like Staycity aparthotel, they have a laundry facility.

I will probably be proved wrong but I am not aware of any Aparthotels in Venice. The vast majority of hotels there are in old palazzi which don't adapt well to that style of accommodation. OTOH there are a lot of apartments which have laundry facilities - I've stayed in two and they both did.

Staycity has one in Mestre, short bus ride.

I think you'll find anything similar to an aparthotel in Rome is in the outskirts.

Personally I'd put location at the top of the list.