In March, the US Court of International Trade ordered customs officials to refund the more than $160bn (£121bn) the government had collected in tariffs, putting roughly 330,000 importers in line for potential reimbursements.
The refunds relate to levies charged under the International Emergency Economic Powers Act (IEEPA).
As of early April, more than 56,000 importers had completed the necessary steps to apply for refunds online when the portal opened, with their claims worth $127bn.
On Monday, one small business owner told the BBC he was able to find his way through the portal just minutes after it opened.
However, another told the BBC’s US partner CBS News, external that when he tried to file a claim he received a message saying: “The system is currently experiencing high volume, please try again later.”
He said the system appeared to be “overwhelmed”.
US Customs and Border Protection has said successful applicants can expect refunds, as well as any applicable interest, to be paid in 60 to 90 days.
However, some individual consumers, who were hit by the tariffs indirectly through higher prices, are not expected to be compensated.