Israel has denied that one of its soldiers had been captured by Hamas in overnight fighting, while the Gaza Health Ministry says the death toll in the Palestinian territory has crossed the 500 mark.
Al-Qassam Brigades, Hamas' armed wing, says it captured an Israeli soldier by the name Shaul Aron late on Sunday, but Ron Prosor, Israel's ambassador to the UN, dismissed the claim, saying that "those rumours were untrue".
Osama Hamdan, a Hamas leader and spokesman, told Al Jazeera that the Israeli soldier had been captured: "Al-Qassam declared all the information about the military operations. When we said we captured the soldier, it's true and everyone has to deal with that as true."
The al-Qassam Brigades did not say whether the captured soldier was dead or alive.
Aron would be the first Israeli soldier held captive in Gaza since 2011, when Israel released more than 1,000 Palestinian prisoners to free Gilad Shalit, a soldier who was held for more than five years after his 2006 capture in a cross-border raid.
Aron was allegedly captured amid overnight fighting in the eastern part of the Gaza Strip, where heavy shelling continued into Monday morning.
At least 75 Palestinians and 13 Israeli soldiers were killed overnight in Gaza's Shujayea neighbourhood. The US state department confirmed that two of the Israeli soldiers were US citizens.
It remains unclear whether they held Israeli citizenship as well.
Israel maintains that its offensive is targeting Hamas fighters in Gaza and a network of underground tunnels which they say are used to attack their troops and civilians.
On Monday, the Israeli army said that "two terrorist squads infiltrated Israel through a tunnel from north Gaza" and that it "killed 10 terrorists".
Spokesperson Peter Lerner told Al Jazeera that the Israeli army hit 16 tunnels with 45 access points so far.
Lerner identified the civilian deaths in Gaza as a "human tragedy", but defended the army's offensive saying that it was "a result of Hamas' policies".
"In this conflict, there is only one party that cares about the civilian population of Gaza and it isn't Hamas [...] They are abusing and exploiting the civilians."
At least 512 Palestinians have been killed since the start of Israel's "Operation Protective Edge" on July 8, of which the UN says the majority were civilians. At least 20 Israelis, mostly soldiers, have also been killed.
Al Jazeera's Nicole Johnston, reporting from Gaza City, said that shelling continued across different areas of the Gaza Strip.
"The people from those neighbourhoods [in the Gaza's east] say that their homes, their district has been destroyed and they're seeking shelter inside Gaza City," she said.
She said that the Gaza Gealth Ministry confirmed that a family home was hit by tank shelling and 17 people were killed, including women and children in Khan Younis, while a four-storey building was hit in Rafah, killing up to nine people, including four children and an eight-month-old baby.
The Security Council expressed concern at the escalation of violence and the growing number of casualties.
Eugene Gasana, Rwanda's UN ambassador, said that the council called for an immediate cessation of hostilities called on both sides to observe international humanitarian law.
"The members of the Security Council emphasised the need to improve the humanitarian situation, including through humanitarian pauses," said Gasana after an emergency meeting.
Ban Ki-moon, The UN secretary-general, condemned the killing of civilians by Israeli shelling on Sunday calling it an "atrocious action".