Taya had established close ties with Israel a few years ago, upsetting large sections of Mauritanians and alienating many Arabs and Muslims worldwide.
An Israeli Foreign Ministry official told aljazeera.net on Thursday that Israel was watching "how things were unfolding in Nouakchott."
"Israel has an embassy there, like many other countries. We are waiting to see how things will unfold," said Mark Regev, a senior Israeli Foreign Ministry spokesman.
Regev said Israel had not made any contacts with the new military rulers.
He strongly denied that Taya's close relations with Israel might have been a key reason for the coup.
On Thursday, the Military Council for Justice and Democracy named the longtime chief of national police forces, Colonel Ely Ould Mohammed Vall, as Mauritania's new leader.
It is not clear what Vall's views are regarding relations with Israel.
Earlier, Israel's ambassador to Mauritania, Boaz Besmuth Bismit said in an interview with the Israeli Hebrew newspaper Yedeot Ahranot's electronic net, the "Ynet," that the Israeli embassy was functioning as usual.
He characterized Israel's ties with the west-north African nation as "very important."
"This is an Arab league country that was by our side through the intifada," Bismit said. "Clearly, there are those who are not interested in this connection, but the connection with the government, the president and the Mauritanian people is very important."
Islamic and nationalist leaders, as well as many ordinary Mauritanians, criticized Taya for developing close ties with Israel and ignoring Israeli repression of the Palestinians, especially during the Aqsa intifada that started in 2000.
Taya harshly cracked down on his opponents, especially the Islamists, placing dozens of activists in prison.
In the West Bank and Gaza Strip, the overthrowing of Taya has been met with satisfaction.
A cartoon in Thursday's edition of the Ram aAlah-based newspaper, al-Ayyam showed a Mauritanian soldier kicking Taya, along with the Star of David, Israel's national symbol.