Opposition leader Benjamin Netanyahu joined the well wishers. "We don't always see eye to eye, but on this issue we are united. I wished the prime minister a quick recovery," he said at a Likud party meeting.
Defense Minister and Labor Chairman Ehud Barak sent a message of his own: "I join all the people who wished the prime minister a quick recovery and I trust he will continue working."
MK Arieh Eldad (National Union-National Religious Party), a physician, said that "Olmert should not resign because of his condition." He added that "this type of illness will not impair his functioning."
Yet, Eldad believes the prime minister should resign "despite the tumor, because of his failures."
MK Ran Cohen (Meretz) praised Olmert for sharing the news about his illness with the public.
"The PM doesn't have to resign because of his condition," Cohen said, "but he must resign because of his decisions during the Second Lebanon War and the police investigations."
Chairman of the Knesset's Constitution Committee, MK Menahem Ben Sasson (Kadima), thinks Olmert can continue working despite the tumor.
"I laud the prime minister for his initiative, the transparency, and his courage," he said, "I wish him a quick, full recovery and I trust his ability to perform his duties."
MK Ahmad Tibi (United Arab List – Ta'al), a physician, said: "Ehud Olmert did the right thing by informing the pubic of his illness." He added that the prime minister's speech was an expression of courage and commitment.
Palestinian negotiator Saeb Erekat also sent his best wishes to Olmert.
"We wish him a speedy recovery, and we hope to continue working with him toward achieving a two-state solution and ending the Israeli occupation that began in 1967," he said.
Erekat's boss, Palestinian President Abbas, is a survivor of prostate cancer.
Olmert thanked all the well wishers during a Kadima faction meeting: "I am unable to return the calls of all those who telephoned me. It is heartwarming and I thank everyone."
Amnon Meranda and AP contributed to this report