Plans to redeploy UK troops to the south of Baghdad to assist US operations have sparked warnings from opposition MPs.
Southern Iraq has been comparatively peaceful
UK troops have been asked to fill in behind US soldiers, it is understood.
On Saturday, Shadow Defence Secretary Nicholas Soames joined opposition calls for a Commons statement on the government's intentions.
The Ministry of Defence has confirmed discussions are taking place but said no decision on movements had been made.
Mr Soames told BBC Radio 4's Today programme the UK must have an "equal say" in US plans to defeat insurgents.
He added: "The question of chain of command is an extremely important one. I've no objection to British troops serving under American command but it needs to be extremely clearly worked out.
"The rules of engagement must be very clear because they may well be different to those which the regiment would have used in Basra."
BBC defence correspondent Paul Adams said it was thought an American unit had been earmarked for "combat operations" in insurgency stronghold Falluja and that the UK Government was now considering the US request for British cover.
If British troops were deployed to cover for the US, it would be somewhere to the south of Baghdad in "a reasonably benign environment", similar to the British army's base in Basra, he said.
The deployment, which would involve up to 650 personnel coming under US command, was expected to last "a few weeks".
Senior military sources had said the move was being seen as a "relatively risk-free option" and as a matter of "being a good ally to the US", he added.
BBC correspondent Claire Marshall said there was speculation the British troops could be deployed to the town of Iskandariya, 25 miles (40km) south of Baghdad, freeing up the 24th Marine Expeditionary Force currently based there to fight in Falluja.
On plans for defeating the insurgents, Mr Soames told Today it was time the "rather supine" impression that America "ordered everything to happen while we just follow along" must "come to an end".
"We have to make sure that we have an equal share in the planning and an equal input into what the Americans decide to do."
BRITISH FORCES IN IRAQ
9,200 troops deployed to the Gulf
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
British soldiers would be among those to "pick up the bill" if the operation went wrong, he added.
He also called on Defence Secretary Geoff Hoon to "stir himself" and make a statement outlining the government's intentions for its troops "to stop the great anxiety" for the families of those involved.
His words echoed those of Tory leader Michael Howard who said on Friday it was "vital that a statement is made in Parliament at the earliest possible opportunity so that we can ask the relevant questions".
Liberal Democrat foreign affairs spokesman Menzies Campbell said any question of putting British troops under US operational command "would be extremely controversial".
"And for a government to take that step without informing the House of Commons in advance would be seen as a dereliction of the government's responsibility," he told BBC News on Saturday.
BBC political correspondent Jonathan Beale said MPs "across the board are concerned for the welfare of troops".
There were concerns that British troops would be "sucked in" to "hot-spots" like Falluja.
And a possible change in the rules of engagement, with a perception that American forces were confrontational compared with the "softly-softly" approach of their UK counterparts, was also causing concern for MPs on all sides.
But the government would "almost definitely" make a statement to the Commons, he added.
One option being considered would involve Scottish troops from the Black Watch Regiment extending their tour of duty in southern Iraq by a short period.
If this option is pursued, the plan would be to have the regiment home in time for Christmas.
Troops are currently acting as the reserve force in the southern city of Basra, and their relatives say they were told they would not be returning home next month as planned.
A MoD spokesman said no decision had been taken to extend their current tour: "Discussions are continuing as these things are always discussed. But if these discussions lead to a decision it will be announced in the normal way."