Their comments come after US Secretary of State John Kerry on Friday said Israeli and Palestinian negotiators had agreed to meet to pave the way for a resumption of direct peace talks, stalled for close to three years.
Israeli media have said that while there will be no formal declaration of a settlement freeze, a key demand of the Palestinians for talks to resume, Prime Minister Benjamin Netanyahu will quietly halt building for the time being.
"We must not have a freeze," Transport Minister Israel Katz, of Netanyahu's own Likud party told public radio. "It would be immoral, un-Jewish and inhuman to freeze the lives of people and their children.
"The official policy is what counts," Katz added. "I am against a freeze and I don't believe that such a thing will happen. Settlement is strong and growing."
The last round of direct talks between the two sides broke down in 2010 over the issue of Israeli settlement building in the West Bank and east Jerusalem.
Housing Minister Uri Ariel of the far-right Jewish Home party, told the radio that he did not want to consider even a limited freeze.
"It's inappropriate for the Jewish people, for the land of Israel and for a sovereign state," he said. "We are in favour of building as much as possible."
Kerry gave away very little detail of the agreement, which came after four days of frenetic consultations with Israeli and Palestinian leaders.
But Palestinian president Mahmud Abbas has repeatedly stressed that his demands of a freeze to Israeli settlement building on occupied land and release of prisoners held by Israel must be met before talks can resume.
Intelligence Minister Yuval Steinitz on Saturday announced that there would be the release a "limited" number of Palestinian prisoners as a "gesture" for the peace talks.
Katz on Sunday took issue with his comments.
"I personally oppose the release of terrorist murderers," he said. "If the matter arises in future in the cabinet I shall vote against it."