He said Hamas had "basically" agreed to US President Donald Trump's proposal and the framework for releasing the hostages, while meetings were underway to co-ordinate the logistics of that.
"They have also agreed, in principle and generalities, to enter into this idea about what's going to happen afterwards," he said.
"A lot of details are going to have to be worked out there."
Rubio said he hopes a deal can be finalised early this week to allow the release of hostages.
"All those talks are occurring, even as I speak to you now, we're hoping it will be finalised very quickly, early this week," Rubio told ABC.
"And I'm hoping, you know again, who knows the timeline? But this cannot take weeks or even multiple days. We want to see this happen very fast."
He said the US would know "very quickly" whether Hamas was serious or not during the current technical talks to co-ordinate the release of the hostages.
"Priority number one, the one that we think we can achieve something very quickly on hopefully, is the release of all the hostages in exchange for Israel moving back" to the yellow line - where Israel stood within the Gaza Strip in the middle of August - Rubio said.
He described the second phase of the long-term future of the enclave as "even harder".
"What happens after Israel pulls back to the yellow line, and potentially beyond that, as this thing develops? How do you create this Palestinian technocratic leadership that's not Hamas?" Rubio said.
"How do you disarm any sort of terrorist groups that are going to be building tunnels and conducting attacks against Israel? How do you get them to demobilise?"
"All that work - that's going to be hard - but that's critical because without that, you're not going to have lasting peace," he added.
Trump told reporters on Sunday that his peace proposal was a great deal for Israel.
Hamas had drawn a welcoming response from Trump on Friday by saying it accepted certain key parts of his 20-point proposal, including ending the war, Israel's withdrawal and the release of Israeli hostages and Palestinian captives.
But the group left some issues up for further negotiation at talks in Egypt as well as questions unanswered such as whether it would be willing to disarm, a key demand from Israel to end the war.
On Monday, indirect talks are expected in Egypt between Israel and Hamas, focusing on a ceasefire and the release of remaining hostages in exchange for Palestinian prisoners as a first step.
An Israeli delegation led by Strategic Affairs Minister Ron Dermer will fly to Egypt on Monday to take part in talks, Prime Minister Benjamin Netanyahu's office said on Sunday.
The negotiations will be held in Egypt's Red Sea resort of Sharm el-Sheikh, Netanyahu's office added in a statement.
A Hamas delegation, led by the group's exiled Gaza Strip chief Khalil al-Hayya, was also expected to land in Cairo to join representatives of the United States and Qatar for talks over the implementation of the effort to halt the conflict.
The plan has stirred hopes for peace among Palestinians but there was no let up of Israeli attacks on the Gaza Strip on Sunday as planes and tanks pounded areas across the enclave, killing at least 16 people, local health authorities said.
Four of those killed were seeking aid in the south of the strip and five were killed in an air strike in Gaza City in the early afternoon, they said.
with AP and DPA
