The Rafah border between Gaza and Egypt is not yet open to foreigners, including Americans, looking to evacuate. But if Americans who want to evacuate can move closer to the border crossing they should do so, because "there may be very little notice if the crossing opens and it may only open for a limited time," a U.S. Embassy spokesperson said.

We will continue to be in touch with private U.S. citizens to determine what assistance we may be able to provide," the spokesperson said.

A senior State Department official said the department is "in touch with a number of the roughly" 500 to 600 Palestinian-Americans "who have expressed interest in receiving information about leaving."

Hamas said nine hostages in Gaza have been killed by Israeli airstrikes over the last day.

The Israeli army and Israeli intelligence said they've targeted and killed Hamas commando forces leader Ali Qadi.

The United States did not ask Israel to hold off or delay a ground invasion of Gaza, ABC News has learned.

“U.S. officials have not asked Israel to slow down. But discussions did include the importance of taking into account the safety of civilians during any operations,” according to a U.S. official.

The official said the Israelis took it under advisement.

-ABC News' Luis Martinez

Hamas fighters are believed to be "still hiding" in some communities in southern Israel even after the Israeli military took back control, according to Israel Defense Forces spokesman Maj. Doron Spielman.

"We are in control of the communities, but we actually assume that there are Hamas terrorists that are still hiding in these areas, including in the road where we are now," Spielman told ABC News during an interview Monday in Sderot, Israel. "In all these communities, we've seen terrorist come out of hiding. Just yesterday, they took over an ambulance."

"We're still being very, very careful," he added. "This is a war zone with active terrorists that are operating here."

Sderot is a southwestern Israeli city located near the county's border with the Hamas-ruled Gaza Strip. A police station there was stormed by Hamas fighters on Saturday as part of the militant group's wider incursion, leaving at least six Israeli police officers dead. The IDF then bombed the police station with the Hamas fighters inside, demolishing it.

Hamas fighters and other Palestinian militants are "striking strategic locations" along the border fence, allowing them to drive through in pickup trucks, Spielman said. Civilians in some of the local communities have been ordered to evacuate, while others have left voluntarily, according to Spielman.

"We do have a lot of ground troops in this area. We have a lot of tanks. We have, in addition, artillery. And we're prepared forever for anything," he said. "And if it happens, the next stage, it's going to happen here because this is the area that was the flashpoint and this is the area we're going to be presenting ourselves and finishing this battle. We, of course, have no choice but to finish."

When asked about the mounting casualties of Palestinian civilians in Gaza as a result of the IDF's retaliatory airstrikes, Spielman said: "We always try to avoid civilian casualties. However, I would say that this is war and our first priority here is to destroy Hamas."

-ABC News' Angus Hines and Ian Pannell