MONTEVIDEO, Dec 4 (Reuters) - Uruguayan President Tabare Vazquez has offered to resign as head of the ruling Socialist Party after he defied its members and vetoed a law decriminalizing abortions in the first 12 weeks of pregnancy, a senator said on Thursday.

His offer to step down comes just days after Congress, which is controlled by the president's party, denounced his veto and vowed to present another bill in next year's session.

Under Uruguay's 1938 abortion law, women who have the procedure face up to nine months in prison while abortion practitioners face up to two years. Abortion is only permitted in cases of rape or when the life of the woman or the fetus is endangered.

Abortions after the first 12 weeks of pregnancy were not under consideration and would still be illegal in Uruguay.

"The offer came in a few days ago. It is a painful decision, both for the president and for us, and we will do everything possible to keep him from leaving," Monica Xavier, a Socialist Party senator, said on local radio.

A doctor and center-left leader, Vazquez has repeatedly vowed to veto the easing of abortion restrictions. Congress passed the measure last month, in a rare move for a predominantly Roman Catholic country.

At the time of his veto, Vazquez said it was more important to help women with unwanted pregnancies than to facilitate abortions for them. Support in Congress was not strong enough to override the veto.

Latin America is home to about half the world's Catholics and abortion is only fully legal in Cuba and Guyana. (Reporting by Conrado Hornos; Writing by Dana Ford; Editing by Fiona Ortiz and Philip Barbara)

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