Were you looking for something like the following?

use strict;
use warnings;
use Data::Dumper;

my $string = "> abcd1234
abcd abcd 
>xyz123 
xyz";


my @substrings = $string =~ /(>.+)/g;

print Dumper \@substrings;
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Output

$VAR1 = [
          '> abcd1234',
          '>xyz123 '
        ];
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In your original posting, you say you ...want the parts from > to the first \n after the > in one string, and \n to the next > in another string. Yet that would yield:

$VAR2 = [
          '> abcd1234',
          'abcd abcd'
        ];
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However, in a reply you say, ...the correct output should be >abcd1234 >xyz123..., and, assuming these are two different strings, this is the output from the above script.