Conservative Party leader David Cameron said he would change the legislation on universal jurisdiction if his party came to power and the coalition has held to the pledge.
Supporters of the Labour amendment argue that the new units would reassure people that the new system would not slow down the arrest of any genuine war crimes suspects.
The proposed amendment is also designed to pacify backbenchers uncomfortable that the legislation could water down the principle of universal jurisdiction for crimes against humanity.
However, some Labour supporters of Israel believe the amendment is dangerous compromise to Labour's Left.
Meanwhile, the veteran Labour campaigner Anne Clwyd has proposed a wrecking amendment, to remove altogether the clause passing responsibility for war crimes arrest warrants to the DPP. This has so far been signed by 30 MPs.
