The government said that it could further relax restrictions if things remained calm.
The use of incentives around the flashpoint mosque, which is in a hilltop compound, comes about a year after flare-ups led to the 11-day Israel-Gaza war in May.
This year, the government has been on high alert after three attacks by Palestinians in Israel in recent weeks, some claimed by ISIS, killed 11 Israelis.
The attacks raised questions about whether the new rules would be cancelled, but Israel’s coalition government has sought to avoid a repeat of last year’s violence with incentives.
“Along with the civilian steps we are taking starting this week toward Ramadan, which we will expand if there is security stability,” Israeli Defence Minister Benny Gantz said.
"We will continue to do whatever it takes to give people a normal life and to protect Israeli citizens from terrorism."
Under the new rules, Palestinian women from the occupied West Bank will be allowed to enter Israel without a permit for Friday prayers at Al Aqsa Mosque.
Palestinian men and boys older than 50 and younger than 12 will be allowed to enter for prayers without a permit. And men between the ages of 40 and 49 with a permit will also be allowed in.
Thousands of Palestinians with close relatives in Israel will also be given permits to visit them between Sunday and Thursday, the government's Palestinian liaison office said.
The rules will apply for the next week and security officials will meet again to consider expanding them further.
Israel announced the rules a few hours after police arrested eight Palestinians accused of throwing rocks and other objects at officers outside the Damascus Gate to Jerusalem’s Old City.
There have been other scuffles near by.
Last year, clashes between police and protesters in and around the Old City helped to spark the Gaza war.
Israeli police are on high alert after the three deadly attacks by Palestinians in Israel in recent weeks.
An Israeli raid on a refugee camp in the occupied West Bank last week in search of a gunman’s suspected accomplices set off a gun battle in which two Palestinians were killed and 15 were wounded.
On Saturday, Israeli police said its officers killed three Palestinian militants who were involved in recent attacks on Israeli forces and were planning another.
Also last week, the government announced $56 million in emergency funding for more police officers and equipment.
Israel captured East Jerusalem, along with its holy sites to the three Abrahamic faiths, in the 1967 Arab-Israeli war and later annexed it in a move unrecognised by most of the international community.
The Palestinians seek East Jerusalem as the capital of a future state that would include the West Bank and Gaza Strip.
Israel considers the entire city its united capital.