Public Security Minister Yitzhak Aharonovitch (Yisrael Beytenu) publicly expressed support for continuing Operation Protective Edge on Friday, at a press conference with Israeli reporters.
"A ceasefire without exposing all the tunnels would be a mistake," he said.
Reports are circulating Friday that Israel and Hamas may accept a US-brokered cease-fire within the next few days, despite the fact that there is no concrete evidence from either side that a truce will be reached.
A deal, according to London-based Arabic newspaper Al-Hayat, may involve capitulating to part of Hamas's unprecedented set of demands - including opening ground and naval borders - but would not see terrorists released.
Aharonovitch denied that Israel was considering a cease-fire just yet, however.
"There are all kinds of proposals," he noted. "The IDF is operating in Gaza and exposing many terror tunnels, and the goal is to expose them all. We need to do what needs to be done, and not limit the IDF to a deadline."
The Political-Security Cabinet had been due to discuss a possible truce deal at noon Friday, but that discussion has been postponed until 3:00 pm.
News of a possible deal surfaces less than one day after Prime Minister Binyamin Netanyahu declared that the operation would continue "at full strength in both the air campaign and land campaign."
Hamas leader Khaled Meshaal declared on Wednesday that Israel must accept his list of unprecedented conditions for a ceasefire in order for any truce to be declared.