The Israeli military says it has expanded its ground operation against Hamas to "every part" of the Gaza Strip.
The army resumed its offensive Friday after a weeklong cease-fire expired.
After focusing its ground operation on the northern part of Gaza in recent weeks, the military began carrying out airstrikes in southern Gaza as well.
The vast majority of Gaza's population has fled to the south in search of safety.
But late Sunday, Israeli military spokesman Daniel Hagari said ground troops were also pushing into the south.
"The Israeli army is continuing and expanding the ground operation against the Hamas presence in every part of the Gaza Strip," he said. "The forces are coming face-to-face with terrorists and killing them."
Earlier, eyewitnesses had told DPA news agency that Israeli ground troops had advanced into an area east of the city of Khan Yunis in the south of the Gaza Strip.
Israel reports 10,000 airstrikes on Gaza since war began
Israel's military says it has conducted around 10,000 airstrikes on targets in Gaza since the war began nearly two months ago.
The Israeli Defence Forces (IDF) said its targets included command centers, tunnels and weapons depots belonging to Palestinian terrorist organizations. The information could not be independently verified.
The announcement comes as international criticism of Israel's actions is growing.
Israel's aeriel bombardment has caused a large number of civilian casualties.
On Sunday, the Hamas-run Health Ministry said some 15,523 people have been killed in Gaza since the war erupted and another 41,316 have been injured.
According to UN estimates, around 80% of the 2.2 million inhabitants of the Gaza Strip have had to leave their homes because of the war.
UNICEF calls for 'immediate humanitarian cease-fire'
The United Nations Children's Fund (UNICEF) said it was witnessing "massive child casualties."
UNICEF spokesperson James Elder was in southern Gaza and said the area was experiencing "the worst bombardment of the war right now."
"I feel like I'm almost failing in my ability to convey the endless killing of children here," he said in a video he posted on social media.