Insert a range of numbers from a call to sp_sequence_get_range
This should be good up to about 2,500 values (depending on version):

;WITH x(n) AS 
(
  SELECT TOP (@variableNumberOfIdsNeeded)
    (ROW_NUMBER() OVER (ORDER BY number)-1) 
    * CONVERT(BIGINT, @SeqIncr)
    + CONVERT(BIGINT, @FirstSeqNum)
  FROM master.dbo.spt_values
  ORDER BY number
)
--INSERT @newIds([NewId]) 
SELECT n FROM x;


If you need more, or are worried about using the view master.dbo.spt_values, see other possible techniques for generating sets without looping here:


Generate a set or sequence without loops – part 1
Generate a set or sequence without loops – part 2
Generate a set or sequence without loops – part 3