* Gaza border simmers as Egypt tried to mediate calm
* Hate crimes underscore stagnant peacemaking efforts (Adds details)
By Ali Sawafta
JERUSALEM, July 4 (Reuters) - Chanting "Intifada, Intifada", thousands of furious Palestinians called for a new uprising against Israel during the funeral on Friday of a teen they believe was kidnapped and killed by far-right Jews.
Stones thrown at Israeli police were met by teargas, stun grenades and rubber bullets in one of the most highly charged displays of enmity in Jerusalem in years as the body of Mohammed Abu Khudair, 16, wrapped in a Palestinian flag, was carried through his neighbourhood under a sweltering sun.
Medics said 15 demonstrators were treated for injuries. There was no immediate word of arrests by the Israelis.
At another flashpoint, the Gaza Strip border, Palestinian rocket and mortar launches, followed by Israeli artillery shelling, persisted on Friday but no one was hurt.
Palestinian officials trying to calm tensions in recent weeks have said they would prevent any intifada, or uprising, and seek a solution to a crisis that began when three Israeli teens were kidnapped in the occupied West Bank on June 12.
The discovery of their dead bodies on Monday prompted an outpouring of national grief in Israel. Tensions spiked after Abu Khudair was kidnapped on Wednesday in his Arab neighbourhood in Jerusalem and his charred body was found hours later in a forest on the edge of the city.
Many Palestinians, including President Mahmoud Abbas, assert he was the victim of far-right Jews incensed at the discovery this week of the remains of the three Israeli teenagers.
With Israel having mobilised ground forces outside Gaza on Thursday in a threat to invade, Egypt tried to mediate a truce. Israel and the Islamist Palestinian Hamas movement each said the other had to back down first.
Israeli Prime Minister Benjamin Netanyahu called Abu Khudair's killing, a day after the three Jewish seminary students were buried, "loathsome" and ordered a swift police investigation. Israeli authorities said they did not yet know whether the Palestinian was indeed the victim of a hate crime.
The slayings of the young Palestinian and Israelis ramped up mutual aggravation that has festered since Netanyahu quit U.S.-sponsored peace talks in April over Abbas's surprise power-share with rival Hamas Islamists.
Netanyahu accused Hamas militants of seizing the three Israelis and the military mounted a 2-1/2-week-long search in the West Bank and a sweep against the movement's activists and institutions. Hundreds of Palestinians, many of them Hamas members, were detained.
Hamas has neither confirmed nor denied involvement in the West Bank kidnappings. That did not stop some of Abu Khudair's mourners calling for more seizures to pressure Israel into releasing Palestinians in its jails.
"Oh (Hamas) Qassam Brigades, avenge, avenge. Do it again and free prisoners," they crowd chanted, along with cries to rekindle an Intifada, or a revolt, which Palestinians last waged a decade ago.
Tensions were further inflamed by Israeli restrictions on Muslim access to the city's al Aqsa mosque complex during the Ramadan fasting month. Only men 50 or older could enter.
The police presence was already heavy throughout the city this week, to control anti-Arab marches by Israeli ultranationalists and stone-throwing protests by Palestinians.
The Israeli military said it had jailed four soldiers for posting anti-Arab messages on social media. A police spokesman said the force's cyber-crime unit was also cracking down on racial incitement online, whether by Jewish or Arab citizens.
While vowing to hit Hamas over the three Israeli teenagers' killings, Netanyahu is reluctant to launch a major operation in that could upend already difficult relations with Abbas.
More powerful Israeli attacks in Gaza could also draw longer-range Palestinian rocket fire capable of reaching Israel's heartland and its business capital, Tel Aviv.
Israeli cabinet minister Yuval Steinitz said any escalation risked disrupting international efforts to negotiate a curb on Iran's disputed nuclear drive ahead of a July 20 deadline.
"We don't want, possibly, to divert all of the world's attention to something else now, of all times, from the matter of the Iranian nuclear programme, which is the existential threat to Israel - more than terrorism, more than riots," Steinitz told Israel's Army Radio on Friday. (Writing by Jeffrey Heller and Dan Williams; Additional reporting by Nidal al-Mughrabi; Editing by Tom Heneghan)