United Nations Secretary General Ban Ki-moon is "gravely concerned" about the rising death toll in Syria, a top official said Tuesday ahead of a U.N. Security Council meeting on the escalating conflict.

Ban wants the Security Council to unite to apply "sustained pressure" on Syrian government to apply the peace plan of U.N.-Arab League envoy Kofi Annan, assistant secretary general Oscar Fernandez Taranco told the 15-nation body.

A previously unknown Islamist group has claimed responsibility for an attack on Israel by militants who crossed from Egypt, according to a video message reported by SITE Intelligence on Tuesday.

The video featured a militant announcing the setting up of a group named the "Mujahideen Shura Council in the Environs of Jerusalem," while other footage showed two gunmen saying they were about to launch the attack, according to the video posted by the US-based monitoring service.

Ousted Egyptian strongman Hosni Mubarak's last prime minister, Ahmed Shafiq, won a presidential election runoff, his campaign team insisted on Tuesday, disputing his Islamist rival's claim of victory.

"We are certain that the next president of Egypt is General Shafiq," his campaign spokesman Ahmed Sarhan told a news conference.

Jordan has tightened border controls to prevent loyalists of Syrian President Bashar al-Assad from infiltrating into the kingdom, an official of the opposition Syrian National Council said on Tuesday.

"Jordan used to have an open border policy with the Syrians, but now new regulations prevent some Syrians from entering the kingdom," Amman-based SNC official Nizar Heraki told Agence France Presse.

The trial of Iraq's fugitive Sunni Vice President Tareq al-Hashemi resumed on Tuesday, with the court hearing testimony that silencers were found in raids on his house and that of his son-in-law.

Lawyers for Hashemi, who has been accused of running a death squad and is being tried in absentia, also officially returned to the trial after withdrawing in May.

Militants from the armed wing of Gaza's ruling Hamas movement on Tuesday said they had fired 10 Grad rockets at Israel in a rare show of force after Israeli raids killed six.

"This is our answer to the Zionist crimes. It will continue if they carry out more strikes on Gaza," a statement said, with a spokesman confirming it was the first time they had fired such longer-range rockets at Israel since April 2011.

France on Tuesday voiced concern that Egypt's military appeared to be clinging to power after a pivotal presidential vote and called for a speedy return to democracy.

Egypt's ruling military council announced de facto martial law just after the election, giving the armed forces control over the legislature and state budget.

Troops pounded and raided rebel strongholds across Syria and clashes erupted in Homs on Tuesday as 36 people were killed in violence nationwide, a watchdog said.

Regime forces clashed with rebels before dawn in Homs where a soldier was killed amid "intermittent shelling" of the central city, said the Syrian Observatory for Human Rights.

The Free Syrian Army Tuesday called on their "Kurdish brothers" to join rebels fighting President Bashar Assad's regime, while promising an end to injtices against Kurds in a future democratic Syria.

"The Joint Command of the Free Syrian Army ... appeals to our Kurdish brothers, soldiers and civilians, and invites them to join the ranks of the FSA inside the country," the group's spokesman Colonel Kassem Saadeddine said in an online video.

Syria on Tuesday accused gunmen of using Homs residents as "human shields" and of blocking government's efforts to evacuate them from the besieged central city.

"Contacts have been made with the head of the U.N. observers and local authorities in order to facilitate the departure of innocent citizens (besieged) in Homs," the foreign ministry said in a statement.