The Stop the War Coalition has staged several protests and will be demonstrating outside the Philharmonic on Friday.
Spokeswoman Audrey White said: "I think Cathy will be admired by many people for standing in solidarity with ordinary Iraqis."
A Philharmonic spokeswoman said: "We've been speaking to a number of artists, including Cathy Tyson who has declined to take part."
Dr Rice will visit Liverpool and Foreign Secretary Jack Straw's constituency of Blackburn on a return invitation after Mr Straw visited Ms Rice's home town of Birmingham, Alabama.
A Foreign Office spokesman said: "The Foreign Secretary is delighted Secretary Rice has accepted his invitation and is looking forward to showing her - and the world - two places which reflect the thriving economy and cultural life of Britain.
"In Liverpool, they will go to the Royal Liverpool Philharmonic, Liverpool Institute for Performing Arts and Maritime Museum, which between them will bring to life for Secretary Rice Liverpool's vibrant, artistic culture and the city's historic transatlantic links with the United States."
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