Ahmed was given Australian citizenship in July and made his debut for the country in the recent Twenty20 series in England.
The spinner has not been wearing the logo of brewing company VB on his shirt, with Cricket Australia having agreed to his request.
Former Australia rugby union international Campese sparked a row with his criticism of Ahmed on Twitter, which was strongly criticised on the social network.
When a fellow Twitter user suggested that Campese's "go home" comment could be considered racist, 50-year-old Campese replied: "well why did he come to Aussie for in the first place. A better life? Now he is telling people what he wants.!"
Now Campese has followed up his remarks from last week by suggesting his words were misconstrued, but also with the promise of an apology that he wants Cricket Australia to relay to Ahmed.
He wrote on Twitter: "Just like to say sorry for a comments. It is about sport and never has or will be about religion. Any who knows me can tell you that.
"I will be ringing the ACA to say sorry and to pass my message on. Sport is about team work and team.that was my point. Sorry again."
Campese is not the only former Australian sportsman to have caused a stir with recent remarks about Ahmed.
Former Australia batsman Doug Walters told the Sydney Daily Telegraph: "I think if he doesn't want to wear the team gear, he should not be part of the team. Maybe if he doesn't want to be paid that's OK."
That led Campese last week to tweet his approval of Walters' comments, writing: "Doug Walters tells Pakistan-born Fawad Ahmed: if you don't like the VB uniform, don't play for Australia. Well said doug. Tell him to go home."
Prior to Campese's initial comments, Cricket Australia chief executive James Sutherland responded to early reaction that had surfaced to Ahmed's request on social media.
Sutherland said: "CA does not condone racism in any way, shape or form. CA is fully supportive of Fawad's personal beliefs and he is a valued and popular member of the Australian cricket team and the wider cricket community."
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