In the same interview, Witkoff emphasized that the US and Israel needed a deadline on the release of the remaining hostages in Gaza.
Hamas appears to be able to secure de facto ceasefires for Ramadan each year and not have to ever do anything in return.
Hamas signals readiness for ceasefire talks as Trump pressures for hostage release.
The Jerusalem Post reported earlier this week Israel would return to fighting in Gaza in about a week and a half, barring a breakthrough in talks.
He also confirmed that a date has been set for a return to fighting, but that he cannot reveal it.
Hamas said that Trump's repeated threats against Palestinians are support for Netanyahu to back out of the Gaza ceasefire and intensify the siege.
A KAN News poll found that Israelis are split on ceasefire talks, Gaza aid, and Netanyahu’s leadership amid ongoing war.
"Special Envoy Witkoff plans to return to the region in the coming days to work out either a way to extend Phase I or advance to Phase II," the spokesperson said.
Israeli source: No expectation for Trump envoy Steve Witkoff to visit Israel • Sources say 'Hamas has neither accepted nor rejected the Witkoff proposal'
"Hamas had also put forward positions for a permanent ceasefire that are totally unacceptable," Netanyahu said in his statement.