"Just like any entity that handles personally-identifiable information, the White House has a responsibility to notify Americans if the recent, or any future breach, results in a compromise," the committee chairman, John Thune, said in a statement on Sunday accompanying the letter.
"If such information has been lost, the White House still has a responsibility to victims even if it believes the hack was perpetrated by foreign spies and not cyber thieves," Thune added.
The White House said last month that a CNN report that Russian hackers penetrated sensitive parts of the White House computer system referred to an incident it disclosed last year, and declined to comment on who was responsible for the breach.
It added that it took immediate measures at the time to evaluate and mitigate the activity.
Asked about the Commerce Committee letter, White House National Security Council spokesman Mark Stroh declined to comment further on the breach, but said: "We have consistently supported timely notification in the event of data breaches, consistent with existing federal policy."
Thune in his letter to Obama said that while hackers did not appear to have accessed classified data, the unclassified computer system reportedly contained sensitive information such as schedules, policy discussions and emails, including exchanges with diplomats.
"This unclassified computer system likely also contains the personally identifiable information of many Americans," the South Dakota Republican wrote, noting that people must submit personal information before being allowed to enter the White House.
© Thomson Reuters 2015