Why not adapt the solution ikegami suggested a few weeks back on the Near equal partitions. thread?

sub ranges_beth2 {
  my ($M, $N) = @_;
  my $r = ($M+1)%$N;
  my $q = ($M+1-$r)/$N;
  my $iEnd=0;
  return [ map { my $iStart=$iEnd; [$iStart, ($iEnd+=$_) - 1]
               } (($q+1) x $r, ($q) x ($N-$r)) ];
}
[download]

Sample output

---------------------------
 0 : from       0 to 9999997 (9999998)
---------------------------
 0 : from       0 to 4999998 (4999999)
 1 : from 4999999 to 9999997 (4999999)
---------------------------
 0 : from       0 to 3333332 (3333333)
 1 : from 3333333 to 6666665 (3333333)
 2 : from 6666666 to 9999997 (3333332)
---------------------------
 0 : from       0 to 2499999 (2500000)
 1 : from 2500000 to 4999999 (2500000)
 2 : from 5000000 to 7499998 (2499999)
 3 : from 7499999 to 9999997 (2499999)
[download]

It ensures that partitions never differ by more than 1 in size and avoids rounding errors. On benchmark results it is also marginally faster (4-8%) than the code in the OP (actual result varies between runs)

       s/iter   buk eli_ik
buk      1.01    --   -8%
eli_ik   0.923    9%   --

         Rate   buk eli_ik
buk    1.02/s    --   -4%
eli_ik 1.06/s    4%    --
[download]

Benchmark code

use Benchmark qw(cmpthese);

sub testRanges {
  my $cr=$_[0];
  for my $M (1..1e2) {
    for my $N (1..$M) {
      $cr->($M,$N);
    }
  }
}

cmpthese(10
       , { 'buk' => sub { testRanges(\&ranges_buk) }
           , 'eli_ik' => sub { testRanges(\&ranges_beth2) }
         }
       );
[download]

Update: added that it avoids rounding errors.

Update: minor revision to account for OP desiring range to go from 0..$M ($M+1 values) not 0..($M-1), i.e. $M values.