Credit card company officials said 14,000 numbers had been posted on line Tuesday and another 11,000 Thursday. However, they said some of the codes had expired and that the active cards were all being cancelled.
The hacker has identified himself as OxOmar and says he is part of a Saudi Arabian hacker team. In a post Thursday he said he had leaked information about more than 400,000 Israelis and said the "Jewish lobby" was hiding the scale of the attack.
Israeli officials say the hacker has also released email addresses and passwords, but have yet to confirm where he is based.
"This incident should be treated as a cyber attack," Justice Ministry official Yoram Hacohen told the Ma'ariv daily.
"?When it comes to digital felonies committed outside the country, it is difficult to locate the perpetrator if he took the correct precautions," Hacohen added.
The data theft was one of the worst that Israel has said it has faced, and while the financial damage was reportedly minimal, the breaches have heightened concerns about the potential use of stolen information by Israel's enemies.
"These matters are worrisome," Science and Technology Minister Daniel Hershkowitz told Israel Radio, calling the incident "a sample of the great danger out in cyberspace."
He added that Israel had "impressive capabilities" and was setting up an agency to deal with the issue, as Prime Minister Benjamin Netanyahu pledged last year.
On the back of the credit card theft, a parliamentary committee has scheduled a session for the coming week to review Israel's readiness to defend itself from cyber attacks.
"We must prepare to cope with cyber threats in anticipation of any attempts to use Internet terror to strike at Israel," said lawmaker Ronit Tirosh, the committee chairwoman.
Some newspaper columnists speculated that hackers might be retaliating for recent attacks in Iran, including the mysterious Stuxnet computer virus that snarled its controversial nuclear computer systems.
"The peculiar incident we are facing could be a bad joke, a youthful prank, a hate-driven terror attack for beginners or the first stage in an Iranian cyber-terror attack," commentator Ben Caspit wrote in Friday's edition of Ma'ariv.
However, Hershkowitz dismissed such speculation, saying: "the imagination tends to soar."
The hacker wrote in his Web post: "So, I've started thinking of sending all Israeli credit cards I own which reaches 1M data."
"Enjoy it world! Purchase stuff for yourself online, buy anything you want," he added.
Dov Kotler, CEO of Isracard, a unit of Bank Hapoalim, said 5,200 credit card numbers listed by the hacker Thursday, belonged to his customers.
The thefts have dampened Internet sales in Israel, media reports said, though no figures were immediately available. Israeli reports have indicated that most of the information stolen had been gleaned from online commercial sites.
(Editing by Crispian Balmer)
Posted by Jason Lomberg, Technical Editor