To load messages for some interval, use the command messages/load_interval:

svc=messages/load_interval&params={"itemId":<long>,
				   "type":<uint>,
				   "ival1":<uint>,
				   "ival2":<uint>,
				   "flags":<uint>,
				   "flagsMask":<uint>,
				   "loadLocations":<bool>,
				   "loadCount":<uint>}

You can find an example of this request in the sample Messages.

Interval types:

• 1:
  ival1 - interval beginning value (or 0)
  ival2 - interval end value (or 0)
• 2:
  ival1 - quantity of messages which will be fetched from the very beggining or from time pointed in parameter ival2
• 3:
  ival1 - quantity of messages which will be fetched to end or to time pointed in parameter ival2

Masks:

{
	"count":<uint>,				/* messages count */
	"messages":[				/* array of messages */
		{
			...		
		}
	]
}

You can find message formats in the chapter Data format: Messages.