SAN FRANCISCO — Federal prosecutors urged an appeals court to let them present evidence they say shows Barry Bonds knowingly used steroids, arguing Monday it was mistakenly thrown out by a trial court judge on the eve of his perjury trial earlier this year.

Among the evidence that prosecutors say is key to their case are three urine samples they say belong to Bonds and tested positive for the steroids, methenolone and nandrolone. Prosecutors allege Bonds’ personal trainer, Greg Anderson, collected the samples for testing at the Bay Area Laboratory Co-Operative, the headquarters of a massive sports doping ring busted by federal investigators in 2003.

In February, U.S. District Court Judge Susan Illston banned evidence connected to Anderson because of his refusal to testify at Bonds’ trial. Anderson has told the judge he would go to jail rather than testify.

Anderson spent more than a year in prison for previously refusing to testify before a grand jury investigating Bonds.

Illston also barred an alleged ‘‘doping calendar’’ kept by Anderson, log books maintained at the lab and other evidence produced by the trainer. The judge said there’s no way to prove the evidence is what the prosecutors say it is without Anderson’s testimony.

Bonds has pleaded not guilty to lying to a federal grand jury investigating BALCO in December 2003 when he denied knowingly taking performance-enhancing drugs.

The government filed its plea Monday with the 9th U.S. Circuit Court of Appeals. The appeal has delayed indefinitely the start of Bonds’ trial.

In its filing, federal prosecutors said Illston erred by excluding the evidence because they can prove the connection to Bonds through his own grand jury testimony and through other witnesses.

‘‘Bonds’ grand jury testimony unequivocally established that as early as 2000, he started giving blood and urine samples to Anderson to deliver to BALCO for the sole purpose of having those samples tested,’’ prosecutor Barbara Valliere wrote in the 64-page filing.

Central to the government’s appeal are three urine tests that tested positive. BALCO executive James Valente has testified that Anderson delivered the urine samples to him and identified them as belonging to Bonds.

Courts do generally exclude such statements as ‘‘hearsay’’ if the speaker doesn’t vouch for them. But there are several exceptions to those exclusions, including whether the disputed statement was uttered by an employee or agent of the suspect.

The trial court judge ruled Anderson didn’t fall into that category because he received sporadic payments from Bonds that appeared to be gifts rather than salary.

Prosecutors disagreed and said Monday that Bonds paid Anderson $15,000 a year and gave him a $20,000 bonus after the slugger broke the single-season homer mark with 73 in 2001.

The government’s court filing said records show Anderson ‘‘was at Bonds’s beck and call nearly every day of the year. It was thus more than sufficient to establish that Anderson was acting as Bonds’s ’servant’ when he delivered the samples to BALCO.’’

Bonds’ attorney Dennis Riordan didn’t return a telephone call Monday. Bonds’ written reply is due July 1.