TEL AVIV, Dec 13 (Reuters) - An Israeli mayor who said he was quitting in protest at the government's failure to stop Palestinian rocket attacks on his town withdrew the resignation on Thursday at the behest of Defence Minister Ehud Barak.

"You can't refuse the defence minister," Sderot Mayor Eli Moyal, who announced he was stepping down during a live radio interview on Wednesday, told reporters after meeting Barak. Moyal's resignation was to have come into effect on Friday.

Militants in the Gaza Strip, seized by Hamas Islamists from their Fatah rivals in June, fire short-range rockets and mortars every day at towns in southern Israel. While few cause damage or injury, the rockets spark widespread panic among residents.

A rocket launched by Palestinian faction Islamic Jihad wounded a woman in Sderot on Thursday. Hours later, Israel's air force killed an Islamic Jihad field commander and two other militants in Gaza City.

Barak's office said in a statement that he told Moyal: "At a time like this, responsibility and commitment to Sderot's residents take precedence over any other consideration".

Moyal's financial dealings have are under police investigation but he has denied any wrongdoing in the case.

(Writing by Dan Williams, Editing by Richard Balmforth)

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