$url = $2;                            <-- called $url here
print "$url\n";
push @urls, $new_url;  # or @new_urls <-- called $new_url here.
[download]

Just rename one.

Also, it seems you want to search for the pattern multiple times. You'll need the "g" modifier for that.

   while ($html =~ m{...}g) {
      my $new_url = $2;
      print "$new_url\n";
      push @urls, $new_url;
   }
[download]