The Gaza Strip's governing Hamas Islamists are incapable of curbing smaller Palestinian militant groups in the territory, a senior Israeli official said on Tuesday.

The remarks by Strategic Affairs Ministry director Yosef Kuperwasser followed exchanges of fire across the Gaza border for which Israel, in line with long-standing policy, held Hamas responsible, though other factions were involved.

Referring to Hamas's violent takeover of Gaza in 2007 from forces loyal to Western-backed Palestinian President Mahmoud Abbas, Kuperwasser told an Israeli security conference the group is not capable of implementing this responsibility.

Hamas won parliamentary elections in 2006.

Officials from the group declined immediate comment.

It is not in control of what happens in Gaza. Islamic Jihad does what it wants, the Popular Resistance Committees does what it wants, and the Fatah military wing does everything it wants, he said, citing sometime Hamas allies who have also chafed at its authority.

Kuperwasser, a former chief analyst for Israel's military intelligence, said such disarray supported Israel's policy of barrier-building along the Palestinian territories, as this signals that the frontier ends here.

Hamas opposes Israel's right to exist, and the two sides fought a month-long war in Gaza in 2008-2009.

(Reporting by Dan Williams; Editing by Louise Ireland)