After thousands of Louisiana customers have been shut out of their state-run college savings accounts for more than a week, state officials said Wednesday that limited access to the accounts has been restored and that the money appears to be secure.

The outage, which officials said was caused by a “cyber incident,” has prevented customers from accessing about 88,000 active savings accounts containing some $1.8 billion, according to state figures from last month. The accounts are part of Louisiana’s 529 education savings account programs, known as START and K12 START, which help families save for college or private school tuition. During the system shutdown, students and families have not been able to withdraw money from their accounts to pay tuition bills.

While scheduled withdrawals a

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