At least 34 people have been killed in Gaza after Israeli army bombardment intensifies on the second day of a ground offensive it says is aimed at destroying Hamas' cross-border tunnels.

Al Jazeera's Stefanie Dekker, reporting from Gaza, spoke of of "relentless and constant thuds" of tank fire across the eastern border of Gaza on Saturday, "with only around 10 seconds between each".

She said the tanks were concentrated along eastern Gaza, bordering Israel, and that there were many civilian casualties in that area.

Heavy Israeli artillery attacks were reported by an Al Jazeera Arabic correspondent across other areas of the enclave. Drones, jets and attack helicopters patrolled the skies.

The Gaza Health Ministry said the death toll over 12 days now stood at 333. That figure included 77 children, 24 women and 18 senior citizens, and that more than 2,385 people have been injured.

In another development on Saturday, agencies said Egyptian soldiers in north Sinai prevented an aid convoy of activists from reaching the Rafah border crossing with the Gaza Strip.

An army officer at the Balloza checkpoint, one of many along the desert highway to Rafah, told an AFP correspondent that the security situation in the peninsula was too unstable to allow the convoy of 11 buses and 500 activists to pass.

There was a brief scuffle between some activists and soldiers but no arrests were made.

Egypt usually keeps the crossing closed, citing a counterinsurgency operation against fighters in north Sinai, but has allowed entry to Palestinians wounded in the 12-day conflict between Hamas and Israel.

The Egyptian military had earlier said it was sending 500 tonnes of food and medical aide to Gaza.

Hamas has refused to accept a ceasefire with Israel until it receives guarantees that border crossings to Gaza - all but one under Israeli control - will be opened.

Earlier in Israel, one civilian was killed and two others were injured by a rocket strike on a Bedouin community near Dimona, bringing the Israeli death toll to two civilians.

The army said that an Israeli soldier was killed in friendly fire earlier in the week.

The intense shelling came hours after the US president, Barack Obama, said the US was "deeply concerned about the risks of further escalation and the loss of more innocent life".

He said he hoped Israel would operate "in a way that minimises civilian casualties".

Success 'not guaranteed'

The ground offensive is a new phase in Israel's Operation Protective Edge operation which the military said would destroy tunnels used by Hamas.

Benjamin Netanyahu, the Israeli prime minister, said the ground operation was necessary to deal with the tunnels, but admitted there was "no guarantee of 100 percent success".

The offensive failed to prevent an incursion by a tunnel into Israel by Qassam Brigades fighter on Friday. The attack was foiled by the Israeli military, however, with one fighter killed.

On the diplomatic front, the Palestinian and Israeli UN ambassadors traded blame for the violence, with Israel's Ron Prosor insisting no other country would "tolerate ... terrorist" rocket fire at its citizens.

Meanwhile, Ban Ki-moon, UN secretary-general, arrived in the Middle East on Saturday to bolster truce efforts, AFP news agency reported.

Ban would help Israelis and Palestinians "in coordination with regional and international actors, end the violence and find a way forward," Jeffrey Feltman, UN under secretary-general for political affairs, told the Security Council.

Fares Akram contributed to this report.