A group of 45 Labour MPs have urged a Commons vote before the Britain agrees to a US request for UK troops to be sent to an area south west of Baghdad.
In a Commons motion the MPs, led by war opponent Alice Mahon, say the move would "significantly increase the risk" to British troops.
Tony Blair has insisted the issue is a military and not a political matter.
The final decision will come after a UK reconnaissance team has visited the area and made its recommendations.
Kidnapped
Redeploying the soldiers would free US troops for an assault on Falluja.
It emerged on Tuesday that the head of operations in Iraq for the charity UK Care International, Margaret Hassan, has been kidnapped in Baghdad.
Mr Blair said Ms Hassan was well-respected and had been doing her "level best" to help Iraq.
The government would do everything it could to secure her release, but did not know which group was holding her, he said.
Britain's chief of defence staff is expected to recommend by the middle of this week whether to comply with America's request for troops to fill in behind its soldiers.
Mr Blair urged people to wait until the scope of any operation were revealed.
He insisted the move was aimed at ensuring Iraq's elections went ahead as planned next January and had nothing to do with the US presidential polls.
"There has been a request by the American military to the British military, not a political request from the US president to me," he added.
'It's too much'
Earlier, Labour MP Eric Illsley told BBC Radio 4's World At One: "It drags us into the US election campaign whether we like it or not."
Fellow backbencher Andrew Mackinlay said he and most of his colleagues did not believe the US was incapable of filling the troops gap with its own forces.
"We have to say thus far and no further," he argued. "We have given 110% and I think they are just asking too much of us."
UK Foreign Secretary Jack Straw said he was "very sympathetic" to the US request for troops, but the final decision would not be taken until the reconnaissance mission reported back.
Earlier on BBC Radio 4's Today programme, Mr Straw said it was a "myth" to claim the current British area of operations was trouble-free while the US region was in turmoil.
A battalion from the Black Watch regiment is believed to have been earmarked for the move.
Nearly 7,500 British troops are currently serving in southern Iraq, based mainly around the port of Basra.
Sandy Caird, the father of one soldier, said families were worried British troops might have to adopt "American" tactics.
He said: "They go in with full force. They don't seem to think things out on the ground the same as what we do."
BRITISH FORCES IN IRAQ
9,200 troops deployed to the Gulf, almost 7,500 in Iraq
1,400 of those are reservists
Most troops in Basra and al Muthanna provinces
1 Mechanised Brigade is currently 'lead formation'
6,315 troops from 10 nations also serve in the area
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Great so Bush wants us to go in and fill in for the Yanks in the most dangerous part of Iraq so that there will be no body bags coming home before the election. And there's not even going to be a vote on this???? I accept that we have to do our job now that we are there but to commit our forces like this so that Bush's election chances are boosted is taking the piss. And to not even allow Parliament to vote...
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