The firm, formed from the merger of Glaxo Wellcome and SmithKline Beecham three years ago, said in a statement it had received a tax bill for $2.7 billion, which the US Inland Revenue Service says is owed by Glaxo Wellcome for the years 1989 to 1996.
The company said it estimated the interest on the full claim to be around $2.5 billion, net of federal tax relief.
The claim follows a long-running dispute with the US tax authorities which had been flagged previously by GlaxoSmithKline (GSK) in its annual report.
"GSK considers that the additional tax claim is inconsistent with the treatment of other pharmaceutical companies, including GSK legacy company SmithKline Beecham," the statement said.
"GSK plans to contest this claim for additional taxes by filing a petition in the US Tax Court, where a trial is not expected until sometime in 2005-2006," it added.
Glaxo said that it expected to receive an additional assessment from US authorities for the 1997-2000 period, as similar tax issues remained open.
Shares in the firm - which made a pre-tax profit of 6.52 billion pounds ($11.9 billion) in 2002 on sales of 21.21 billion - were 0.6 percent down at 12.53 pounds by 0850 GMT, off lows of 12.38.
Industry analysts said the muted stock market reaction to news of the huge tax claim reflected the fact that the dispute - if not the sum - was already well known.
One analyst said other multinationals had settled similar disputes with US tax authorities on relatively benign terms.
A GSK spokesman said the firm was not required to pay the amount immediately and pointed out that the company had been making provisions for tax liabilities during the past few years.
He declined to reveal the extent of the provisions.
Before receiving this notice, the company said it had attempted to resolve the dispute by referring it to negotiations between the US and UK tax authorities.