GAZA, Aug 22 (Reuters) - Israel and the Islamist group Hamas, which controls the Gaza Strip, have agreed to a ceasefire after five days of cross-border violence, officials said on Monday.

One official who was involved in mediating talks between Israel and Palestinian factions in Gaza said the groups had reached an understanding on a truce and that the truce has started.

A Palestinian official said Hamas had agreed to ensure the recognition of the ceasefire by smaller militant groups which were responsible for most of the rockets fired at Israel in the latest surge in violence.

Israeli Prime Minister Benjamin Netanyahu's security cabinet had met earlier on Monday and decided the military would cease its strikes in the Gaza Strip if militants there halted attacks on Israel, according to an Israeli official.

Like similar arrangements in the past, the truce is not a formal agreement, but consists of each side saying it would halt hostilities if the other side did the same.

The violence erupted on Thursday when militants crossed into southern Israel and carried out a series of deadly attacks on vehicles on a quiet desert road. More than 30 people were killed in those attacks and subsequent rocket attacks and air strikes. (Reporting by Nidal al-Mughrabi; Editing by Tim Pearce)