The Biden administration says the current positions presented by Israel and Hamas allow the gaps in hostage deal and ceasefire negotiations to be closed and put a deal within reach, White House spokesman John Kirby said in a briefing with reporters.

Why it matters: A deal would lead in the first phase to the humanitarian release of up to 33 hostages held by Hamas in Gaza in return for up to 42 days of ceasefire and the release of about 800 Palestinian prisoners.

What they're saying: Kirby said that after assessing the positions of the parties the Biden administration thinks they can close the remaining gaps.

• Unlike the optimism expressed by Kirby, the Israeli assessment is that the gaps are wide and that Hamas' leader in Gaza, Yahya Sinwar, didn't give his negotiating team flexibility for the next round of indirect talks taking place today in Cairo.
• Israeli officials say Sinwar's main goal has not changed: to reach a deal that will force Israel to end the war in Gaza. Israeli Prime Minister Benjamin Netanyahu vehemently refuses that.

Our thought bubble: Kirby's optimistic statement seems to be part of a White House strategy to create a negotiations dynamic that could lead to a hostage deal and a ceasefire.

Catch up quick: Hamas announced on Monday that it accepted a ceasefire proposal given to it by Egypt and Qatar.

• The announcement came after several days of talks between Hamas officials and Egyptian and Qatari mediators in Cairo over the weekend and on Monday in Doha.
• CIA director Bill Burns was in Cairo and Doha when the talks were taking place and weighed in with the Egyptians and the Qataris, according to sources familiar with the talks.
• U.S. officials say Hamas' statement came after the group presented its counteroffer to an Israeli proposal from late April.

Israeli officials said the Hamas response was basically a new proposal drafted by the group together with Egypt and Qatar and claimed it goes far beyond the proposal that Israel submitted at the end of April and that won the support of the US, Egypt and Qatar.

• Israeli officials claim the Biden administration knew about the changes during the negotiations process but didn't brief Israel before Hamas announced it accepted it on Monday.
• A senior U.S. official pushed back saying "American diplomats have been engaged with Israeli counterparts. There have been no surprises."

Driving the news: An Israeli delegation arrived in Cairo on Tuesday to hold talks with the Egyptian and Qatari mediators, Israeli officials said.

• The officials said a Hamas delegation also arrived in Cairo to hold follow-up talks with the mediators.
• CIA director Bill Burns arrived from Doha to Cairo to follow the talks for up close, Kirby said.
• He is expected to then travel to Israel on Wednesday, a source with knowledge of the trip told Axios. He is expected to meet with Netanyahu and other Israeli officials.

Between the lines: Senior Israeli officials said that despite the disappointment with the American and Egyptian conduct in recent days, Israel decided to send the delegation to Cairo to examine whether Hamas's position is final or if it is a basis for negotiations.

• A senior Israeli official said that the Israeli team went to hear from the Egyptian and Qatari mediators and to ask for clarification on a long list of issues included in the Hamas response.
• "The delegation traveled to understand the depth of the gap and the level of flexibility that Hamas has. They will come back and report and then we will see what Israel is required to do," the senior Israeli official said.

Editor's note: This story has been updated with details about CIA director Bill Burns' travel to Israel.