* Abbas condemns "massacre"; death toll from conflict tops 400
* Israel says area housed rockets, locals warned to evacuate
* U.N.'s Ban to see Abbas in Qatar, tour region in truce bid (Updates death toll, adds collapse of humanitarian ceasefire)
By Nidal al-Mughrabi and Jeffrey Heller
GAZA/JERUSALEM, July 20 (Reuters) - At least 62 Palestinians were killed on Sunday in Israeli shelling of a Gaza neighbourhood that left bodies strewn in the streets and thousands fleeing for shelter to a hospital packed with wounded, Palestinian witnesses and officials said.
The Israeli military said militants from Gaza's dominant Hamas group responded with anti-tank missiles and heavy weapon fire in some of the bloodiest fighting since Israel launched its Gaza offensive 13 days ago.
A two-hour "humanitarian ceasefire" in the area, agreed by both sides at the request of the International Committee of the Red Cross, broke down in minutes with each side blaming the other.
Palestinian President Mahmoud Abbas accused Israel of carrying out a massacre and declared three days of mourning.
The Israeli military said Hamas had fired rockets and built tunnels and command centres in Sheja and that it had warned locals to evacuate two days earlier. Its ground forces were backed up by air strikes and artillery, the army added.
Anguished cries of "Did you see Ahmed?" "Did you see my wife?" echoed through the courtyard of Gaza's Shifa hospital, where panicked residents of Shejaia gathered in family groups. Inside, bodies and wounded lay on blood-stained floors.
Elderly men there said the Israeli attack was the fiercest they had seen since the 1967 Middle East war, when Israel captured Gaza.
Shifa hospital's director, Naser Tattar, said 17 children, 14 women and four elderly were among the 62 dead, and about 400 people were wounded in the Israeli assault.
DEATH TOLL TOPS 400
Gaza's Health Ministry officials said at least 403 Palestinians, many of them civilians, have been killed and about 2,600 wounded in the 13-day offensive, that Israel says it launched to halt mounting cross-border rocket fire by militants.
On Israel's side, two civilians have been killed by cross-border fire and five soldiers have died in fighting. More than 50 Israeli troops have been wounded, hospital officials said.
Thousands fled Shejaia, some by foot and others piling into the backs of trucks and sitting on the hoods of cars filled with families trying to get away. Several people rode out of the neighbourhood of 100,000 in the shovel of a bulldozer.
Video given to Reuters by a local showed at least a dozen corpses, including three children, lying in rubble-filled streets, though the footage could not be verified independently.
As the tank shells began to land, Shejaia residents called radio stations pleading for evacuation. An air strike on the Shejaia home of Khalil al-Hayya, a senior Hamas official, killed his son, daughter-in-law and two grandchildren, hospital officials said.
Israel, which has accused Hamas of using civilians as human shields by launching rockets from residential areas, sent ground forces into the Gaza Strip on Thursday after 10 days of air, naval and artillery barrages failed to stop the salvoes.
The military said it beefed up its presence on Sunday, with a focus on destroying missile stockpiles and a vast tunnel system Hamas built along the frontier with Israel.
"It has been a tough day of combat, but it won't deter us," Israeli Finance Minister Yair Lapid said, without referring to events in Shejaia.
"The operation is necessary and, if needed, we will broaden it," he told reporters while visiting wounded Israeli soldiers in a hospital in the southern city of Beersheba.
Egypt, Qatar, France and the United Nations, among others, have all been pushing for a permanent ceasefire, with little sign of progress.
Militants kept up their rocket fire on Israel on Sunday. Sirens sounded in southern Israeli towns and in the Tel Aviv metropolitan area. There were no reports of casualties on the Israeli side.
Qatar was due to host a meeting between Abbas and U.N. Secretary-General Ban Ki-moon on Sunday, a senior Qatari source told Reuters. Ban was due to travel to Kuwait, Egypt, Israel, the Palestinian Territories and Jordan during the week, a U.N. statement said.
The Qatari source said Abbas would also meet Hamas leader Khaled Meshaal.
Western-backed Abbas in April struck a reconciliation deal with Hamas, which seized the Gaza Strip in 2007 from forces loyal to his Fatah movement. The agreement led to the formation of a Palestinian unity government and Israel's pullout from U.S.-brokered peace talks.
Hamas has already rejected one Egyptian-brokered truce, saying any deal must include an end to a blockade of the coastal area and a recommitment to a ceasefire reached after an eight-day war in Gaza in 2012.
Hostilities escalated following the killing last month of three Jewish students that Israel blames on Hamas. Hamas neither confirmed nor denied involvement.
The apparent revenge murder of a Palestinian youth in Jerusalem, for which Israel has charged three Israelis, further fuelled tension. (Additional reporting by Noah Browing in Gaza and Ari Rabinovitch in Jerusalem; Writing by Jeffrey Heller)