The march comes just two days after Netanyahu was ousted after 12 straight years in power, toppled by an ideologically divided coalition including, for the first time in Israel's history, an Arab party.
Palestinian Authority Prime Minister Mahmoud Shtayyeh also cautioned Israel against letting the march go ahead.
The May 10 - Jerusalem Day - attack, which came amid already rising tensions over planned East Jerusalem home evictions and police actions against Muslim rioters on the Temple Mount, touched off 11 days of intense fighting between Israel and Hamas-led terrorists in the Gaza Strip, as well as a rash of lower-level clashes in the West Bank and mob violence between Arabs and Jews inside Israel. Israeli media reported that police will allow participants to congregate outside the Old City's Damascus Gate but will not let them cross through it to the Muslim Quarter, which has an overwhelmingly Palestinian population. Hamas called on Palestinians to "resist" the march.
The so-called March of the Flags celebrates the anniversary of the city's "re-unification" after Israel captured its east, including the Old City which houses sites holy to all three Abrahamic faiths, in 1967.
"We warn of the unsafe repercussions that may result from the occupying power's intention to allow extremist Israeli settlers to carry out the Flag March in occupied Jerusalem tomorrow", Shtayyeh tweeted in English.
On Thursday, clashes broke out between East Jerusalem protesters and Israeli police, as far-right lawmaker Itamar Ben Gvir marched to Damascus Gate.
And it says Hamas is responsible for what happens in Gaza.
Mansour Abbas, whose Raam party is the first Arab faction to join an Israeli coalition, said the march was "an attempt to set the region on fire for political aims", with the intention of undermining the new government.
Damascus Gate is a focal point of Palestinian life in east Jerusalem.
Palestinians want East Jerusalem, which includes the Old City, to be the capital of a state they seek to establish in the occupied West Bank and Gaza.
When the march was originally announced for last week, senior Hamas official Khalil Hayya warned it could spark a return to violence like that of May 10-21.
It urged people to gather in the Old City and at the Al-Aqsa Mosque to "rise up in the face of the occupier and resist it by all means to stop its crimes and arrogance".
Hamas and other militant groups in Gaza did not immediately respond with rocket fire into Israel, but the situation along the Israel-Gaza border remains extremely tense, and the possibility of an imminent and serious escalation can not be ruled out.
Abu Malek, one of the young men launching the balloons, called the move "an initial response" to the march.
Omer Bar-Lev, the new Cabinet minister who oversees police, said he met with police, military and top security officials to review the plan.