This should do.
Change fn to actual file path of Original csv.
Sub test()
Dim rng As Range, i As Long, ws As Worksheet, n As Long
Const fn As String = "c:\z-test1\samplewkbk.csv" '<- alter to suite
Set ws = ThisWorkbook.Sheets(1)
Set rng = Workbooks.Open(fn).Sheets(1).Cells(1).CurrentRegion
For i = 2 To rng.Rows.Count Step 2000
ws.Cells.Clear
Union(rng.Rows(1), rng.Rows(i).Resize(2000)).Copy ws.Cells(1)
ws.Copy: n = n + 1
With ActiveWorkbook
.SaveAs Replace(fn, ".csv", "_" & Format$(n, "000") & ".csv"), xlCSV
.Close False
End With
Next
rng.Parent.Parent.Close False
Sheets(1).Cells.Clear
End Sub
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