The new deal requires Israel to halt plans to annex land sought by Palestinians, but it has caused controversy.
Anger over the deal led to protesters in Pakistan and Iran making new threats about the accord, which will see the Emirates become only the third Arab nation to recognise Israel.
On Sunday, the chief of staff of Iran's armed forces called the UAE's decision a "disaster".
Mohammad Hossein Bagheri urged Abu Dhabi to "revise" its position or the Iranian military may take a different approach to the nation.
He did not elaborate on what that approach would entail.
"If an incident happens in the Persian Gulf and violates the national security of the Islamic Republic of Iran, even a tiny bit, and we see it from the UAE, we will not tolerate it," Mr Bagheri said.
But for Dubai's small expatriate Jewish community, which has worshipped for years at an unmarked villa, the calls represented more than just the convenience of being able to directly dial loved ones in Israel.
"There's a sense of a miracle upon a miracle upon a miracle, as all of these hurdles fall away and people at last can come together and start talking," Ross Kriel, the president of the Jewish Council of the Emirates, told The Associated Press.
Direct telephone calls from Israel have been blocked in the UAE since its founding in 1971.
That backed the standing position of Arab nations at the time, that Israel must first grant concessions to the Palestinians before being recognised.
sraeli Communications Minister Yoaz Hendel issued a statement "congratulating the United Arab Emirates on removing the blocks".
"Many economic opportunities will open now, and these trust-building steps are an important step toward advancing states' interests," Mr Hendel said.
Israeli news websites that had previously been blocked by UAE authorities, like the Times of Israel, the Jerusalem Post and YNet, can be accessed without using means to bypass internet filtering in the Emirates.
Israel and the United Arab Emirates announced last Thursday they were establishing full diplomatic relations.
The historic deal has delivered a key foreign policy victory to US President Donald Trump as he seeks re-election, and reflects a changing Middle East where shared concerns about Iran have largely overtaken traditional Arab support for the Palestinians.
However, Palestinians maintain it puts a just resolution of the Middle East conflict even farther out of reach.
