The government has asked an independent mediator to look at whether skilled British workers were unfairly debarred from contract work.
Derek Simpson, the joint chief of Unite, Britain's biggest union, said: "Whether you call it indefensible or not, a lot of people find it understandable in the circumstances."
Brown's 2007 pledge to safeguard "British jobs for British workers" has come back to haunt him at a time when he is urging the world to avoid a retrenchment into protectionism.
Total issued a statement on Sunday evening saying it was operating in line with EU rules and British law.
"It has never been, and never will be, the policy of Total to discriminate against British companies or British workers," it said.
Total said that it would work with its sub-contractors to ensure British workers were considered for any vacancies.
Peter Mandelson, the UK business secretary, welcomed the statement and said he hoped it would help to head off further protests.
"[It] should go a long way to meeting people's concerns, should reassure them and allow them to call off the unofficial action that we've seen in the last few days," he told BBC News 24.
Unemployment is rising sharply in Britain, up by 131,000 to 1.9 million in the three months to November.
Industrial unrest is spreading across Europe, fuelled by a worsening economic downturn.
In January, French workers also protested for more pay and job security while Greek farmers set up roadblocks, demanding compensation for the fall in price of their product.