The law -- which aims to correct the "historical mistake" of sending Jews into exile in 1492, forcing them to convert to Catholicism or burning them at the stake -- came into effect in October 2015 and was set to expire in October 2018.
But government spokesman Inigo Mendez de Vigo said Spain's cabinet had agreed to extend the measure by one year until October 2019.
So far 6,432 Jews with Spanish ancestry, who are known as Sephardic Jews, have obtained Spanish citizenship without having to give up their other nationality, he told a news conference following a weekly cabinet meeting.
The Spanish government had estimated when the law was passed that roughly 90,000 people would apply for citizenship, although officials said there was no precise way of knowing how many descendants meet the criteria.
Applicants do not have to be practising Jews but they must have their Jewish heritage vetted by the Spanish Federation of Jewish Communities, a private umbrella organisation for Jewish groups, or by rabbis where they live.
They also have to pass tests on Spanish language and culture, as well as prove they have a "special connection" to Spain but do not have to live in the country.
Before the law was passed Sephardic Jews had to, in most cases, live in Spain for two years before they could obtain Spanish citizenship and had to give up their existing citizenship, which put off many potential applicants.
While Jewish groups welcomed the law when it was passed, some Jewish leaders complained that the requirements were too burdensome.
The government said in a statement it had extended the law due to the "difficulties" applicants faced in obtaining the necessary documents and "the time needed to pass the tests".
Though estimates vary, historians believe at least 200,000 Jews lived in Spain before the Catholic monarchs Isabella and Ferdinand ordered them to convert to the Catholic faith or leave the country.
Many who refused were burnt at the stake.
Up to 3.5 million people around the world are thought to have Sephardic — Hebrew for "Spanish" — Jewish ancestry.
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