The board of the Biennale of Sydney says "artists must make a decision according to their own beliefs" after artists threatened to pull out over a sponsor's links to offshore detention centres.
However, directors indicated they would stand by the sponsor.
In an open letter on Wednesday night, 28 Australian and international artists urged the board to abandon major sponsor Transfield.
The company has contracts with the Department of Immigration to provide security and management services on Nauru and Manus Island.
In the letter the artists said Transfield's involvement in the Biennale had cast a cloud over the event.
"We urge you to act in the interests of asylum seekers," says the letter, which was sent on Wednesday.
The board issued a statement on Friday saying "Artists must make a decision according to their own understanding and beliefs. We respect their right to do so".
Transfield Services is a part of Transfield Holdings' privately owned portfolio of businesses.
Biennale chairman Luca Belgiorno-Nettis is an executive director on the advisory board at Transfield Holdings.
In its response to the artists, the board expressed loyalty to Belgiorno-Nettis.
"We unanimously believe that our loyalty to the Belgiorno-Nettis family and the hundreds of thousands of people who benefit from the Biennale must override claims over which there is ambiguity," the directors said.
The family was a long-time patron of Australian art and vital to the Biennale, the board added.
"The only certainty is that without our founding partner, the Biennale will no longer exist."
The biannual event commences in venues across Sydney on March 21.
