Israel said its closure of the flashpoint shrine, which is holy to Jews and Muslims alike, was a temporary measure aimed at calming tempers.
But Palestinian president Mahmud Abbas condemned it as an Israeli "declaration of war".
Last night's shooting incident and the subsequent killing of the suspected gunman sent tensions soaring to a new high, following months of almost daily clashes between Palestinians and Israeli police in the occupied eastern sector of the Holy City.
"This dangerous Israeli escalation is a declaration of war on the Palestinian people and its sacred places and on the Arab and Islamic nation," Abbas said through his spokesman Nabil Abu Rudeina, warning it would only fuel "more tension and instability."
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Jordan's Islamic affairs minister Hayel Daoud said it amounted to a case of Israeli "state terrorism". Under its 1994 peace treaty with Israel, Jordan has responsibility for Muslim holy sites in Jerusalem.
Meanwhile, residents of the Jerusalem neighbourhood of Abu Tor were left reeling after an early police raid killed Muataz Hijazi, 32.
Israel said he was behind the attempt to gun down hardline activist Yehuda Glick, who has lobbied for Jewish prayer rights at the Al-Aqsa compound.
Police said Hijazi began shooting at officers who returned fire, killing him. But his family had a different version.
"They burst into the house shortly before 6:00 AM, ransacked Muataz's room and then shot him on the roof," said his brother Khalil, 34.