Your stored proc returns a result set I assume, so I assume you're asking if you can do something like:
INSERT INTO TABLE (COLUMNS)
To my knowledge, no, you can't do that. What you can do is create a temp table or table variable, insert it into that table, and then from there, you can insert the values you want into your table.
DECLARE @TempTable TABLE
INSERT INTO @TempTable (AllColumnsFromStoredProc)
INSERT INTO RealTable (ColumnsToInsert)
SELECT ColumnsToInsert FROM @TempTable