Italian Prime Minister Silvio Berlusconi appears to be making good on his promise to deal with crime and immigration, launching a nationwide police sweep just weeks after taking office.

Can I replace the bolded words with keeping his promise and retain its meaning?

I think so, but the "making good on" does carry some extra nuance, maybe that there was some period where it was unsure whether or not the person was going to keep the promise.
Thank you, Gordon.