Kerry condemned the shooting of Yehuda Glick, a US citizen, at the Menachem Begin Heritage Center in Jerusalem, saying the State Department was seeking more information from the authorities.
The site was closed to all visitors on Thursday, as tensions spiraled in the wake of the attempted assassination of rightwing activist Glick in Jerusalem on Wednesday, and the subsequent killing of his suspected attacker in East Jerusalem early Thursday morning.
Glick, a religious activist, was shot and wounded late on Wednesday. He has campaigned for Jews to be allowed to pray at the Al-Aqsa compound, or Temple Mount, a holy site at the heart of the violence.
"It is absolutely critical that all sides exercise restraint, refrain from provocative actions and rhetoric, and preserve the historic status quo on the Haram al-Sharif/Temple Mount - in word and in practice," Kerry said in a statement.
The United States also urged all sides in Jerusalem to exercise restraint, and said it was working with Israelis, Palestinian and Jordanians to try to restore calm.
State Department spokeswoman Jen Psaki also condemned the shooting of Glick, who holds both Israeli and US citizenship. She called for the reopening of the Al-Aqsa mosque to Muslim worshippers, just before police said the compound was now open again.
"We're extremely concerned by escalating tensions across Jerusalem and particularly surrounding the Haram al-Sharif, Temple Mount," Psaki said.
She told reporters that a "continued commitment by Israelis, Palestinians and Jordanians to preserve the historic status quo at this holy site is critical."
US Secretary of State John Kerry was expected to be in touch with Prime Minister Benjamin Netanyahu in the next 24 hours, Psaki added.
Reuters and AFP contributed to this report