Israel's renewed campaign of strikes in the Gaza Strip will continue until all remaining hostages are released, an Israeli official told ABC News.

Hamas said it accepted a proposal from mediators to release one living American-Israeli hostage and the bodies of four dual-nationals, but Israel cast doubt on the offer.

Israeli forces have withdrawn to buffer zones inside Gaza, hundreds of thousands of displaced Palestinians have returned to northern Gaza and hundreds of trucks of aid entered daily until Israel cut off supplies to the territory's 2 million people two weeks ago. Hamas is believed to be holding 24 living hostages and the bodies of 35 others.