The subject is closely watched in Israel, where the Jewish population is deeply concerned with maintaining a Jewish majority.
"In 2015, for the first time, the general fertility rate of Arab and Jewish women was the same and stood at an average 3.13 children," a CBS statement said.
The figures include Palestinians living in Israeli-annexed east Jerusalem as well as Arab Israelis, who account for some 17.5 percent of the country's population.
The CBS said that at the end of 2015 there were 2.798 million children in Israel, accounting for 33 percent of the 8.6 million population.
Of the total under-18 population, 71.3 percent were Jews and 25.7 percent were Arabs, it said.
The remaining three percent were described as "others", including non-Arab Christians.
Among arguments fielded by Israeli proponents of a sovereign Palestine alongside the Jewish state are that the alternative is a single binational state in which Arab Israelis and Palestinians combined would form the majority.
Among the most vocal was the late president Shimon Peres who challenged rightwing calls for Israel to annex the occupied West Bank where more than 400,000 Israelis live among 2.6 million Palestinians.
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"Without a Jewish majority, it is doubtful whether a Jewish state can remain Jewish," he warned in 2012.
There are 1.7 million combined east Jerusalem Palestinians and Arab Israelis.
Arab Israelis, Israeli citizens who largely identify as Palestinians, are the descendants of Palestinians who remained on their land after the creation of Israel in 1948.
The two ethnic blocs are at the moment equally balanced at about 6.4 million each, counting both Israel and the Palestinian territories.
According to the CBS, within Israel, the Jewish birthrate has been growing consistently while that of Arab Israelis has been falling.
In 2000, the Arab fertility rate in Israel was 4.3 children per woman, while the Jewish rate was 2.6 and the Jewish birthrate is expected to outstrip that of Arabs in the near future.
One reason for the steady growth in Jewish births is the high rate among the ultra-Orthodox and Orthodox Jewish populations, where the biblical injunction to "be fruitful and multiply" is taken very seriously.
Another is a continuing response to the massive depopulation of European Jewry during the Nazi Holocaust, encouraging an ethos where bringing more Jewish children into the world is a social and patriotic duty.
Government policy reflects this with generous funding for fertility treatment.
Experts have also pointed to Arab women in Israel having fewer children as their levels of equality have risen in recent years.