Speaking to Likud lawmakers, Sharon said he accepted the results of the party referendum, but hinted that he would press forward with the proposal. Likud voters rejected his plan by a 60-40 margin in Sunday's referendum.
Only half the 193,000 Likud members voted.
Despite a strong endorsement from President Bush, Sharon was unable to sell his Gaza withdrawal plan to his own party, reports CBS News Correspondent Robert Berger. Voters couldn't come to terms with dismantling 21 Gaza settlements.
"Crushing defeat," read a headline in the Maariv daily.
"I can't see that peace will come from this, and I can't uproot my fellow Jew," said voter Tsuri Aldman.
There were no jubilant cheers, no victory speeches, in the Gaza settlement bloc of Gush Katif, after the Likud vote was announced, because of the murder of a pregnant mother and her four daughters, ages 2 through 11, reports the Jerusalem Post.
Israel killed four Palestinian militants in the West Bank and destroyed a Hamas-affiliated radio station in Gaza in missile strikes.
The settlers realize that Sharon is likely to pursue his evacuation plan, but say they will fight it until the end.
"It seems to me that it is going to be a very interesting sitting, a sitting [parliament session] during which we shall have make some tough decisions in the party caucus and in the parliament which will impact on the futures of us all," Sharon said at the opening of the parliament's summer session.
He repeated a pledge made Sunday to consult with Likud ministers and lawmakers, as well as other political parties, to discuss how to move forward.
"I want to emphasize that the people of Israel chose us to find the way to quiet, security and peace and to improve the economy of Israel," Sharon said. "I intend to do that. There is no other reason for us to be here in the Knesset."
His aides say he won't resign.
"The prime minister has clearly stated that he has committed himself to President Bush to carry out this plan," said spokesman Avi Pozner. "Mr. Sharon is well decided to go on with this plan."
Sharon did not say explicitly whether he would continue with his "unilateral disengagement" plan, which calls for a withdrawal from all 21 Gaza settlements and uprooting four settlements in the West Bank.
But allies suggested after Sunday's vote he would look for ways to get around the Likud's veto. The referendum was not legally binding.
Sharon is leaning towards formulating a limited settlement removal plan, reported Maariv Online, the Web site of an Israeli newspaper.
According to the plan, Sharon will initially remove only isolated settlements in Gaza where most residents are interested in leaving. Likud sources say they believe Sharon would be able to pass this type of watered-down plan even with the current makeup of the government.
Justice Minister Yosef Lapid of the centrist Shinui party said he spoke with Sharon earlier Monday and that the prime minister assured him he had not changed his position.
"Sharon promised to fulfill our request to hold a discussion on the issue in the Cabinet," Lapid said. "It isn't possible to leave the political situation frozen."
Though the Palestinians want Israel out of Gaza, they're not sorry about the defeat of Sharon's Gaza withdrawal plan.
"In effect the plan was to make Gaza an open air prison," said Palestinian spokesman Michael Tirazi.
The Palestinians feared that Sharon was abandoning Gaza in exchange for annexing large parts of the West Bank. Now the Palestinians are calling on Sharon to negotiate a Gaza withdrawal with them, instead of taking unilateral steps.
Sharon's defeat within his own party may spur the opposition Labor Party to push for early general elections.
"It turns out that Sharon, whether or not he likes it, does not have a mandate from his own party," said leader Shimon Peres. "The nation must thus be given a chance to vote on the matter."
He also said it was unfair that the Likud Party make a decision on the withdrawals for the entire country.