The arrest came amid tensions between Jews and Arabs in Jerusalem over access to the Al-Aqsa mosque compound, located in the Israeli-occupied east of the city and holy to both Judaism and Islam.
The man, identified as Adam Everet Livix and said to be a Christian and native of Texas born in 1984, has been charged with possession of weapons and being in the country illegally.
"Shin Bet (internal security) and police arrested an American citizen on November 19 who was illegally in Israel, for possession of weapons and planning terrorist attacks," a statement said.
"The suspect admitted during questioning to having suggested committing attacks on Muslim holy sites in Israel," the statement added, saying "weapons stolen from the Israeli army were found in his home".
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The police said Livix was wanted in the United States on a drug-related matter and that his arrest was made in collaboration with the US Federal Bureau of Investigation.
The statement said Livix had lived in the Palestinian Territories in 2013, where he was allegedly approached by a Palestinian to try to assassinate US President Barack Obama during his visit to the region last year.
He moved to Israel illegally a year and a half ago, it said.
The arrest comes against the backdrop of months of rising tensions marked by a series of deadly attacks in Jerusalem and elsewhere.
The Al-Aqsa mosque compound is known as Temple Mount to Jews and as Al-Haram Al-Sharif to Muslims. The heightened tensions stem, in part, from some Muslims reacting strongly to what they perceive as Jewish attempts to take it over.