I am removing an old Asko washer that plugs into single outlet 20 amp box.
The new Samsung washer requires "AC 120 V / 60 Hz / 15 AMP fuse or circuit breaker."
Can I safely replace the 20 amp receptacle with a 15 amp configuration receptacle?
Actually, you don't need to change anything. All 120V 20 Amp receptacles are designed to accept 120V 15 Amp and 120V 20 Amp plugs. Because of that, all 120V 15 Amp devices are normally designed to work properly in a 120V 15 Amp or 120V 20 Amp circuit. This is true for appliances like a washing machine but even for something as small as a cell phone charger that actually uses < 1 Amp.
Once you get past 20 Amp, the design of the sockets change so that you can't mix and match. And you can't plug a 20 Amp device into a 15 Amp receptacle - it won't fit.
Bottom line: No problem.
Read the manual closely and see if it requires a dedicated circuit.
If it doesn't, you may plug right into the existing socket and go. 15A appliances are allowed on 20A circuits unless their instructions say otherwise.
If it does, then the notice in the manual may need to be taken a bit more seriously.
On a dedicated circuit, you have precisely one socket (so you must get one of those odd "single sockets") and since there is only one socket, the breaker and receptacle must agree (this is one time a 15A socket is not allowed on a 20A breaker).
The breaker would have to be changed out to match the socket, I.e. both 15A. The good news is, the wire in the wall can stay the same; it is surely 12 AWG which is larger than required, but larger wire is always allowed.
Just go with what you got and plug it and use it.