The Chicago Tribune was more optimistic, however. It quotes medical sources as saying "that the diagnosis should not keep Mr Giuliani from continuing his Senate campaign", because the illness has been discovered early.
Mr Giuliani, the mayor of New York, has been considered the strongest possible Republican candidate to contest the New York Senate seat against First Lady Hillary Clinton.
"The disclosure of a cancerous condition called into question Giuliani's political status," adds the Washington Post.
According to the newspaper, Mr Giuliani may now have to withdraw from the Senate race "at the eleventh hour", leaving the Republican Party without a strong candidate.
The Chicago Tribune was more optimistic, however. It quotes medical sources as saying "that the diagnosis should not keep Mr Giuliani from continuing his Senate campaign", because the illness has been discovered early.
The New York Post also hints that Mr Giuliani will not drop out of the race. According to one of his aides, the mayor is "simply reserving his options in case of medical complications down the road."
'Critical times'
However, the New York Times calls it "critical times for options" and says that Mr Giuliani "must make some pivotal decisions about his Senate candidacy rapidly".
It points out that the state's Republican Party is meeting on 30 May to nominate its candidate to run against Mrs Clinton.
It is "far from clear what Mr Giuliani might end up doing as he faces the difficult task of unweaving this tangle of medical and political decisions", the New York Times says.
The newspaper also notes that the announcement came at a time when the Republicans were increasingly concerned that "the mayor did not really have his heart in the race" that will force him to leave "the best job he would ever have".
If this is true, the newspaper suggests, then "this unfortunate turn for Mr Giuliani could allow him to make a graceful exit from an unwanted race".
'Political colossus'
The Los Angeles Times calls Mr Giuliani's announcement a "setback for the tough former federal prosecutor, who is the dominant political figure in New York", while the Washington Post calls him "the perfect political colossus to take on the first lady".
The Washington Post writes that "the news about his illness is the biggest personal blow for Giuliani", whose rating has dropped from a comfortable lead over Mrs Clinton to a virtual tie.
"I have no idea," he said when asked if he was going to take part in the Senate race, and added: "I hope that I'll be able to run."
According to the Washington Times, Mr Giuliani's campaign manager said that his election travel schedule would go ahead as planned.
The New York Daily News says that "if the mayor remains in the race, he faces the challenge of running the nation's biggest city, running for Senate and battling to recover his health, all at once".