$seqs =~ /^(>.*)>/ms
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This will grab everything from the start of the string (assuming the string starts with >, upto but not including the last >.

While technically correct, reading between the lines the OP probably wants to grab the data in chunks that start with >. (Otherwise, substr would have been a better choice, no?).

You have to make the * non-greedy. Better to just use a negated character class...

I see that davorg's suggestion is what I was heading for..