One of the laws approved on Sunday shields US citizens from war crimes prosecution in the International Criminal Court, the state news agency Petra reports.
The other law is directed at fighting terrorism financing, Aljazeera's correspondent said.
The Jordanian parliament witnessed heated debates between those opposing what they consider double standards in the interpretation of "terrorism" and those supportive of a law they view as advancing Jordan's political and economic interests, Aljazeera added.
Petra said the law was approved on Sunday by a majority in the 110-member house, without giving a breakdown of the vote.
MPs who voted in favour argued that its approval served the political and economic interests of Jordan without harming its sovereignty, according to Petra.
Amnesty International and Human Rights Watch (HRW) last month appealed for the proposed law to be voted down.
In July, the house threw out the government bill that endorses a deal with Washington to give US citizens immunity from prosecution by the ICC. But it was endorsed by the upper house, which sent it back to the lower house.
King Abdullah II has signed a
US immunity agreement
Ali Abu-Sukar, a Jordanian lawmaker, told the AP: "The agreement contradicts the Rome accord ... and in our days the Americans are the people who now commit war crimes."
Abu-Sukar is a member of Jordan's largest opposition group, the Islamic Action Front, which is the political arm of the Muslim Brotherhood Movement.
"It is humiliating and will twist arms because the United States had threatened to cut economic aid to countries which reject this agreement," he said.
Amnesty and HRW said: "Jordan's parliament should reject an agreement that would shield US citizens and personnel under Jordan jurisdiction from ICC prosecution for war crimes, crimes against humanity or genocide.
In its July rejection, the lower house said the bill "undermines the sovereignty of Jordan", a key Arab ally of the US and a main recipient of US financial assistance.
Washington vehemently opposes the ICC, the world's first permanent tribunal for war crimes and crimes against humanity.
Jordan remains one of America's
staunchest allies among Arabs
The US has waged a global campaign for immunity pacts since the court came into existence in July 2002.
It has threatened to cut off aid to countries that refuse to sign bilateral immunity deals.
The US fears the court could become a forum for politically motivated prosecutions of US citizens, especially soldiers deployed abroad.
Jordan's King Abdullah II signed the so-called Article 98 immunity agreement during a visit to Washington last December.
At the end of August, George Bush, the US president, waived for six months a restriction on millions of dollars in aid to Jordan, which could have been blocked over Amman's membership in the ICC.