"We support the (trade) commission and the commissioner fully in terms of their attempts to try and resolve this issue," Blair's official spokesman said, declining to be identified in keeping with government policy.
Blair will discuss the dispute on a visit to Beijing for an EU-China summit next week, the spokesman said.
The dispute underlines Blair's belief in "the need for Europe as a whole to modernize to meet the challenge from China and India," the spokesman said.
"As we saw in this case, the pace of change is picking up speed all the time and therefore as a continent we have to meet that challenge, as a country we have to meet that challenge," he said.
Mandelson a longtime friend and adviser to Blair has warned that a June textiles agreement reached with China was at risk unless the shipments piling up at European ports were allowed to go to retailers.
Officials from his trade office plan to present proposals to EU governments before the end of the week, with the aim of resolving the impasse as soon as possible, preferably before the summit.
European retailers have warned that the holdup could cause job losses and bankruptcies.