WASHINGTON — With less than a week left for people to sign up for health insurance, the Obama administration said Tuesday that it would allow more time for those who had tried to apply but were blocked by technical problems with the federal exchange.

Several states running their own exchanges, including Maryland, Minnesota and Nevada, have taken similar steps in the last two weeks.

Open enrollment was scheduled to end on Monday for all Americans. The White House had previously insisted that the deadline was firm and would not be extended.

Under the move planned by the administration, some people will be given a special enrollment period, beyond the deadline, if they can show they were not able to enroll because of an error by the federal exchange or by the Department of Health and Human Services. Federal officials allowed a special enrollment period, on a case-by-case basis, for some people who were unable to meet the Dec. 24, 2013, enrollment deadline for coverage starting Jan. 1 of this year.