"It's good that he has faced justice and justice has been done. I think we should reflect on whether we can extradite faster," Cameron told BBC radio.
A New York jury convicted the Egyptian radical on 11 kidnapping and terrorism charges yesterday, and he will almost certainly face a life sentence.
Hamza had previously been an imam at a mosque in north London known for his inflammatory rhetoric and backing for hardline Islamist groups. He was first arrested in 2004 and convicted for hate speech and inciting murder in 2006.
He was finally extradited to the United States in 2012 following an eight-year process that was delayed by appeals to the European Court of Human Rights primarily on the grounds he could face the death penalty in the US.
"Speeding up extradition... we need to look at the avenues of appeal that there are and make sure that those are gone through more quickly," said Cameron.
"We also need to look... at the European Convention on Human Rights, and the position that we've got to get into where, if someone threatens our country, we should be able to deport them if they have no right to be here and that is absolutely essential that we restore that."
He promised to take "big steps" if he is returned to office in the May 2015 general election.
Cameron said Britain had a good domestic record in terms of prosecuting and convicting people guilty of terror offences in Britain, saying several hundred had been jailed.
"Every year since I've been prime minister, our security services and police have managed to prevent at leat one major plot that could have done untold damage to our country and the people who live here."
Mustafa Kamel Mustafa, better known as Abu Hamza al-Masri, had been charged with the 1998 abduction of Western tourists in Yemen, providing material support to Al-Qaeda, assisting the Taliban and sending terror recruits to Afghanistan.