The Labour leader, opening a new exhibition devoted to the Holocaust diarist Anne Frank at Southwark Cathedral, south-east London, said there was a "very strong case" for such a measure and he was giving "active consideration" to it.
His comments come as a Labour MP, Mike Gapes, prepared to introduce a Bill that would make it an offence to deny the Holocaust.
About 6 million people died in the genocide carried out by Nazi Germany, mainly against Jews. But some right-wing historians question whether the massacres really took place. Under the Holocaust Denial Bill, which stands no chance of becoming law under this government, such claims could result in a prison sentence.
Mr Blair said: "There is a very strong case that denial of the Holocaust should be a specific offence.
"This will stand alongside our commitment to strengthen the laws against incitement to racial hatred."
However, making denial of the Holocaust a criminal offence raises questions of free speech and is questioned by some Jewish organisations. Anthony Lerman, of the Institute for Jewish Policy Research, said: "I think this Bill will have a lot of problems in drafting, defining Holocaust denial."
Mr Gapes said countries such as Germany and Austria already had laws making it an offence to deny the Holocaust.Reuse content