By Parisa Hafezi and Michelle Nichols

NEW YORK (Reuters) - Iran has no issue with the U.N. nuclear watchdog's inspection of its nuclear sites, Iranian President Ebrahim Raisi said on Wednesday, days after Tehran barred multiple inspectors assigned to the country.

"We have no problem with the inspections but the problem is with some inspectors ... those inspectors that are trustworthy can continue their work in Iran," Raisi told a press conference on the sidelines of the U.N. General Assembly.

Iran's move was a response to a call led by the United States, Britain, France and Germany at the International Atomic Energy Agency's (IAEA) Board of Governors earlier this month for Tehran to cooperate immediately with the agency on issues including explaining uranium traces found at undeclared sites.

"Tehran's decision was in reaction to some unfair statements by the Western members of the IAEA," Raisi said.

U.N. nuclear watchdog chief Rafael Grossi has condemned Iran's "disproportionate and unprecedented" move.

Tehran's move, known as "de-designation" of inspectors, is allowed; member states can generally veto inspectors assigned to visit their nuclear facilities under the nuclear Non-Proliferation Treaty and each country's safeguards agreement with the agency governing inspections.

(Writing by Parisa Hafezi; Editing by Christian Schmollinger and Lincoln Feast.)