The United States is still working to determine how many Americans remain unaccounted for after Saturday's attack on Israel by Hamas and whether any are among those being held hostage in the neighboring Gaza Strip, according to National Security Council spokesman John Kirby.

In an interview Tuesday with ABC News' George Stephanopoulos on "Good Morning America," Kirby said the number of unaccounted Americans in Israel "keeps changing" as families contact the U.S. Department of State.

"We're trying to get a handle on where they are and how they are," he added. "Sadly, we have to accept the possibility -- the grim possibility -- that some of those unaccounted for Americans could be among those being held hostage by Hamas."

So far, U.S. officials have confirmed that at least 11 Americans were among those killed in Israel over the weekend when Hamas fighters stormed into the country from Gaza. U.S. officials are "preparing for the very distinct possibility that there'll be more" American deaths," Kirby said.

Meanwhile, there's currently no specific information on whether any Americans were among those taken hostage, according to Kirby. Israeli authorities have estimated that Hamas is currently holding "between 100 to 150" hostages in Gaza, including Americans.

"We're working at this really, really hard, talking to the Israelis every single day -- almost every hour -- to try to get more information about the Americans that are unaccounted for," Kirby said, "but we just don't know where they are."

U.S. officials have reached out to their Israeli counterparts to offer assistance in the form of intelligence and hostage recovery expertise, according to Kirby.

"It remains to be seen if there's Americans in that group, what more can be done," he said. "If there's Americans being held hostage, we'll do everything possible to get them home to their families where they belong."

When asked whether the U.S. would be prepared to pay ransom, Kirby said: "I don't want to get too far ahead of where we are."

"We don't even know if there are Americans in this population of hostages," he added.

An Israeli airstrike hit near the Rafah border crossing between Egypt and the Gaza Strip on Tuesday for the second time in two days, Palestinian authorities said.

"The occupation aircrafts re-bombed the gate of the Rafah crossing between the Palestinian and Egyptian sides after it was repaired yesterday, preventing the departure and arrival of passengers," Iyad Al-Bozom, spokesman for the Palestinian Ministry of Interior, said in a statement.

Operations at the frontier were disrupted on Monday after an Israeli airstrike hit near the border on the Gaza side. Officials on the Egyptian side of the Rafah crossing on Tuesday asked crews on the Palestinian side to immediately evacuate the crossing following threats to hit it, according to Al-Bozom.

-ABC News' Ayat Al-Tawy

Iranian Supreme Leader Ayatollah Ali Khamenei said Tuesday that Tehran was not involved in Hamas' recent incursion on Israel but hailed the attack.

"We kiss the hands of those who planned the attack on the Zionist regime," said Khamenei, who was seen wearing a Palestinian scarf in his first televised speech since Saturday's attack.

"The Zionist regime's own actions are to blame for this disaster," he added.

Iran, which does not recognize Israel, has acknowledged giving financial and moral support to Hamas, the militant group that controls the Gaza Strip.

-ABC News' Somayeh Malekian

Israeli ambassador to the United Nations Gilad Erdan said "between 100 and 150" hostages are currently being held by Hamas in the Gaza Strip.

"We estimate a number that is between 100 and 150. I think it’s an unprecedented number," Erdan told CNN during an interview late Monday. "It includes Americans. We don't know the exact number."

A State Department official said Monday night that the department has offered 4,000 American citizens and their immediate family members help to depart Israel via government-organized transportation since Friday.

“Since Oct. 13, we have augmented the limited commercial flight availability by offering more than 4,000 seats on U.S. government-chartered transport by air and sea to U.S. citizens and their immediate family members,” one official said. “We have communicated the availability of departure assistance options for U.S. citizens via targeted, individualized messaging as well as via broad public messaging.”

Departing flights, though, were not nearly at capacity, the official said.

“The departure options we have offered have generally departed at half capacity or less. Nearly 1,000 U.S. citizens and their immediate family members have departed on U.S. government-chartered transport,” an official said.

The official added that 3,000 other American citizens have told the State Department that they were able to leave Israel and the West Bank on their own.

-ABC News’ Shannon Crawford