Obama condemned the firing of rockets into Israel from Gaza and affirmed Israel's right to defend itself, the statement said.
Any U.S. effort to help negotiate a cease-fire faces a key hurdle: The U.S. refuses to negotiate directly with Hamas, which Washington considers a terrorist group.
"Our long-standing policy of having no contact with Hamas has not changed," National Security Council spokeswoman Caitlin Hayden said Thursday evening.
In the past, the U.S. has dealt with Hamas through intermediaries, most notably Egypt. Officials said they would explore a similar approach this time.
"There are players in the region with whom we could work," Hayden said.
Egypt's military government has tense relations with Hamas, unlike the previous leaders in Cairo, who negotiated a cease-fire in the last round of fighting between Israel and the Palestinian militant group, in November 2012.
Senior Obama administration officials said the U.S. thought the Egyptians might still be able to play a role in negotiations, but they also listed the governments of Qatar and Turkey as possible intermediaries. They spoke on condition of anonymity to comment on diplomatic talks.
In addition to the phone call between Obama and Netanyahu, Vice President
The announcement that the U.S. might get involved comes after three days of escalating fire in which Israel has launched numerous air assaults on Gaza, killing scores of Palestinians, and militant groups have fired hundreds of rockets at Israeli towns and cities.
Israel had stepped up its aerial offensive on the Hamas-controlled coastal enclave, and Palestinian militants have unleashed volleys of rocket fire on Jerusalem, Tel Aviv and other cities.
Medical officials in Gaza reported more than 22 people killed Thursday, bringing the campaign's toll among Palestinians to at least 89 dead and more than 600 injured. No Israelis have been killed, and the injuries reported so far have mostly been light.
Egypt, meanwhile, opened the Rafah border crossing with the Gaza Strip to allow injured Palestinians to seek treatment at Egyptian hospitals, officials told the Egyptian state news agency.
The crossing has been closed often for security reasons since Egyptian President
Rafah is Gaza's only border crossing that is not controlled by Israel.