Careful examination of the file c:\arduino-1.5.1r2\hardware\arduino\sam\cores\arduino\wiring_analog.c showed that the function analogRead() always finished with disabling of the analog channel. This is completely unnecessary, if the analog inputs are used only for streaming read from the ADC.
It was enough to comment out the line 164 where the disabling operation of the analog channel executes:
163: // Disable the corresponding channel
164: // adc_disable_channel (ADC, ulChannel);
Only one this comment dramatically increased the speed of the ADC. Now the function analogRead () holds less than 2 uS. Reading 12 channels in FOR loop now takes exactly 24 uS. This is with analogReadResolution(12). I think that for many applications this is sufficient.
However, for such a relatively powerful processor, as SAM3X8E, the low-level code inserting into Arduino will always be necessary. We need more new libraries to use all features of this processor.
Thanks all for advises.