* Group rejects statement in name of its armed wing
* U.N. peacekeepers in Lebanon urge restraint (Adds comment from U.N. peacekeeping force)
BEIRUT, July 13 (Reuters) - The Palestinian group Hamas had no role in a rocket attack on Israel from Lebanon and had nothing to do with a statement in the name of its armed wing that claimed responsibility for the salvo late on Saturday, Hamas officials in Lebanon said.
Three rockets fired from Lebanon hit open areas near Nahariya in northern Israel on Saturday evening. Israel responded with artillery fire. There were no casualties. The attack followed a similar rocket attack from Lebanon on Friday.
Were Hamas behind the attack in question, it would have marked its first such military action across the Lebanese-Israeli frontier.
The attacks from Lebanon coincided with an Israeli offensive on the Hamas-run Gaza Strip that Palestinian officials say has killed at least 160 people. Militants in Gaza have fired hundreds of rockets into Israel during the latest hostilities.
A U.N. peacekeeping force in Lebanon said there had been no immediate claim of responsibility for the attack from Lebanon and urged maximum restraint. UNIFIL, the peacekeeping force, said it had "intensified patrols across the area of operations to prevent any further incidents".
Two Hamas officials in Lebanon said the group was not behind the attack.
Asked about a claim of responsibility issued in the name of the Izz el-Deen al-Qassam Brigades - the Hamas armed wing - Hamas official Osama Hamdan said: "We denied it and said Hamas had nothing to do with this statement."
The claim of responsibility had been circulated in a text message received by journalists in Gaza, the way the Izz el-Deen al-Qassam Brigades often makes such announcements.
A Lebanese security official said investigators had yet to determine who fired the rockets. The main Palestinian factions in Lebanon had told the investigators they were not involved in the attack, the official said.
In its first statement since the eruption of the latest hostilities, the powerful Lebanese group Hezbollah praised Hamas and Islamic Jihad and said it backed the Palestinian "resistance in its goals and steps".
The Iranian-backed movement, which fought a month-long war with Israel in 2006, said the Palestinians had created "a balance of fear" that would pave the way to a "new era" in the struggle with Israel.
While Hezbollah routinely states its readiness for a new confrontation with Israel, analysts believe it is keen to avoid one for now as its fighters aid President Bashar al-Assad's forces in their conflict with insurgents in Syria. (Reporting by Tom Perry in Beirut and Nidal al-Mughrabi in Gaza, editing by Mark Trevelyan)