Palestinian Islamist group Hamas said talks Monday with UN diplomats supporting a fragile month-old ceasefire had gone badly, accusing Israel of a lack of will to end the humanitarian crisis.

The crowded Mediterranean territory, home to around two million Palestinians under an Israeli blockade since 2007, was devastated by 11 days of conflict.

UN Middle East peace envoy Tor Wennesland arrived in Gaza on Monday for talks with Hamas leaders, one month on since a ceasefire between Hamas and Israel came into force.

But a source in Hamas, who asked not to be identified, said the UN envoy had also delivered a "negative message" from Israel to Hamas, without giving further details.

"The meeting was bad, it was not at all positive," the head of Hamas' political wing, Yahya Sinwar told reporters.

"They listened to us attentively, but there are no signs that there are intentions towards solving the humanitarian crisis in the Gaza Strip," Sinwar added.

The UN declined to comment.

Sinwar said leaders in Gaza would meet in "the coming hours" to decide their next step.

Israel said it had allowed Monday the "limited export" of farm produce from Gaza to begin Monday, as well as trucks carrying clothes and fabrics to leave.

But Sinwar said it did nothing to change the situation in Gaza, saying Israel continued to block international aid, as well as critical fuel deliveries needed for the electricity plant, and restrict movement including fishermen in the Mediterranean.

"It is clear that the occupation (Israel) continues to practise its policies against us and our people in the Gaza Strip," Sinwar said.

"We told the representatives of the United Nations that we will not accept this matter."

The ceasefire went into effect May 21, ending the bloodiest fighting between Israel and Hamas since 2014.

The conflict killed 260 Palestinians including some fighters, according to Gaza authorities.

In Israel, 13 people were killed, including a soldier, by rockets fired from Gaza, the police and army said.

Last week, ceasefire violations included Palestinian militants setting off incendiary ballons to spark fires in farm land -- and Israel responding with two rounds of air strikes.