Kerry made the assessment after his second meeting with Palestinian President Mahmoud Abbassince arriving in Amman on Tuesday to press on with efforts to revive negotiations frozen since 2010 in a dispute over Israeli settlement building on occupied land. Israel announced a new expansion on Wednesday.
"We have been able to narrow these gaps very significantly," Kerry told a news conference in the Jordanian capital, Amman.
"And so we continue to get closer and I continue to remain hopeful that the sides can soon be able to come and sit at the same table," he added without elaborating.
Abbas was due to meet other PLO (Palestinian Liberation Organisation) leaders in the West Bankcity of Ramallah on Thursday ahead of a decision on whether negotiations with Israel should resume, Palestinian officials said.
The Palestinian leader has given no public indication of his intentions. But Jordanian Foreign Minister Nasser Judeh said a wider group of Arab officials had offered a strong endorsement of Kerry's efforts after meeting the U.S. diplomat in Amman.
Neither US nor Palestinian officials have given details of the discussions between Abbas and Kerry. Israel has also said little this week but announced a step that clashed with US peace efforts - the granting of initial approval on Wednesday for the construction of 732 new homes in Modiin Ilit, a West Bank settlement midway between Jerusalem and Tel Aviv.
Abbas has said settlement expansion must stop before talks with Israel can get under way. Israeli Prime Minister Benjamin Netanyahu has called on him to return to negotiations unconditionally.
A positive Palestinian decision, if one were to emerge on Thursday or soon thereafter, would be the first tangible sign of progress in Kerry's nearly six-month drive to revive the Israeli-Palestinian peace process, now largely overshadowed by upheaval in Egypt and civil war in Syria.
At the news conference, Kerry again held out the prospect of the rewards Israel could reap in a deal leading to the creation of a Palestinian state in territory it captured in the 1967 Middle Eastwar.
He said Israel should consider carefully a 2002 Arab League peace initiative that it rejected in the past.
"Israel needs to look hard at this initiative, which promises Israel peace with 22 Arab nations and 35 Muslim nations - a total of 57 nations that are standing and waiting for the possibility of making peace with Israel," he said.
The plan, put forward by Saudi Arabia at an Arab League summit in Beirut in 2002, offered full recognition of Israel but only if it gave up all land seized in the 1967 Middle East war and agreed to a "just solution" for Palestinian refugees.
Softening the plan three months ago, a top Qatari official raised the possibility of land swaps in setting future Israeli-Palestinian borders. Israeli Foreign Minister Tzipi Livni said at the time it was "good news that should be welcomed".
Jordanian foreign minister Judeh told the news conference that Arab League officials had been impressed by Kerry's ideas:
"It was an excellent meeting," he said.
"A statement was issued that delivered a strong appreciation of the commitment of the Obama administration and Mr. Kerry to achieve peace and reach a two-state solution that sets up a Palestinian state alongside Israel and guarantees security for the countries of the region."
Palestinians want deliberations on a future state to be based on lines that existed before Israelcaptured the West Bank and East Jerusalem in the 1967 Middle East war, but they have voiced a readiness for possible territorial trade.
Netanyahu has called the pre-1967 war boundaries indefensible. He has not spoken about land swaps but he has said not all settlements would remain in Israeli hands under a future peace agreement.
One compromise mooted in the Israeli media has been a U.S. statement declaring the pre-1967 lines a foundation for peace talks, and Netanyahu voicing reservations but effectively accepting that position.
Israeli officials said they were unaware of any plans by Kerry to visit Israel on his latest trip, and some diplomats and Middle East analysts are sceptical that the Israelis and Palestinians will resume peace talks soon.
The core issues that need to be settled in the more than six-decade-old dispute include borders, the fate of Palestinian refugees, the future of Jewish settlements in the West Bank and the status of Jerusalem.
Most countries consider Israel's settlements on occupied land illegal, a view it disputes.
The European Union said on Tuesday it would bar financial assistance to Israeli organisations operating in the occupied territories, a move Israel's prime minister denounced as meddling in bilateral relations with the Palestinians.