But the bank's boards said in a statement they could not endorse the Royal Bank of Scotland bid either because of "significant unresolved questions." The boards said they may yet decide to favor one offer or the other.
The Royal Bank of Scotland bid, mostly in cash, was worth $96.6 billion at Friday's closing share prices, while the Barclays bid, mostly in shares, was worth $87.5 billion.
Either deal would be the largest in the history of the financial industry.
The decision marks a significant break with the bank's previous policy, which has been to favor the Barclays bid.
ABN also reported net profit for the second quarter of $1.59 billion, down 4.1 percent from $1.66 billion, due to higher taxes and a decline in its mortgage businesses which is being sold in a deal due to close in the third quarter.
Operational earnings rose in line with analysts' expectations.
The results did not show an exodus of ABN Amro staff or customers due to the uncertainty surrounding the bank, as some analysts had feared. The ABN Amro boards praised the Barclays bid as "consistent with ABN Amro's . . . strategic vision."
In addition, Barclays recently announced strategic cooperation with China Development Bank "should further enhance the growth opportunities of a potential combined Barclays/ABN Amro group in the attractive Asian market and could result in creation of additional longer-term value for ABN Amro shareholders."
However, the boards said the financial difference between the two bids was simply too great to ignore.
Chief executive Rijkman Groenink, who prefers the Barclays bid despite the higher Royal Bank of Scotland offer, said Barclays shares were trading at an "extremely low" level and he could envision a scenario in which they would rise enough for Barclays bid to pass the Royal Bank of Scotland-led group bid in value.
That would require an increase of around 18 percent from the $13.78 they closed at yesterday.
Questioned by reporters on why he thought Barclays' shares might rise so much, Groenink said he didn't know they would. "I don't have a crystal ball," he said at a press conference after the results were released.
ABN Amro shares rose 0.29 percent to $47.73 yesterday, midway between the two bids, signifying ongoing doubt by investors as to which will prevail.
Under the Royal Bank of Scotland bid, Fortis NV of Belgium would take ABN's Dutch operations, Banco Santander Central Hispano SA its Brazilian and Italian arms, and Royal Bank of Scotland the rest, including ABN's investment banking arm.
The battle for ABN has been stretching on for months since it announced plans to be acquired by Barclays in March. After RBS signaled in April that it intended to make a higher offer, Groenink agreed to sell ABN's US arm, LaSalle Bank Corp., to Bank of America Corp. for $21 billion.
The surprise move was widely seen as a poison pill measure to frustrate Royal Bank of Scotland, which also wanted LaSalle.
It led to a rebellion by ABN shareholders who saw Groenink's favoritism toward a less lucrative deal as a betrayal of their interests.
A spate of lawsuits by shareholder groups and competing banks followed, freezing the takeover fight for two months.
Ultimately, the Dutch Supreme Court ruled the LaSalle sale was legal and binding, and the RBS consortium pushed ahead with its higher offer anyway on July 18.
Groenink was sidelined from direct negotiations, and ABN has promised not to unexpectedly sell any more operations.
Last week, Barclays increased its offer to narrow the gap somewhat with Royal Bank of Scotland.
Yesterday, ABN said it has amended its agreement with Barclays and "will now be free to discuss the consortium offer with the consortium and its advisers."
Groenink said the company must hold an extraordinary shareholders' meeting at least eight days before Royal Bank of Scotland's bid expires on Oct. 5, putting it on Sept. 27 at the latest.
Four days before that time, by Dutch law, the boards must give a "reasoned opinion" to shareholders about the bids, with or with out a recommendation.