In a statement on Sunday, parliament demanded that the Islamic Action Front "question its four members about the visit (to al-Zarqawi's home), put an end to these practices and consider any attempt to bypass the right, dignity and declared positions of this country a crime that won't go unpunished".
It said the visit was calculated to deliberately provoke the Jordanian people.
Mohammed Abu Fares and three other members of the Islamic Action Front - all parliament deputies - visited al-Zarqawi's home on Friday to pay condolences to his family.
Abu Fares called al-Zarqawi a "martyr" in a sermon he delivered at a mosque following the wake.
He said later that the term did not apply to Jordanians who died in last November's triple hotel blasts in Amman. The attacks were claimed by al-Zarqawi's group.
"Mobs and ignorant people"
"I can't describe them as martyrs; these were mobs and ignorant (people)," Abu Fares told Al Arabiya satellite station on Saturday.
Parliament argued that Abu Fares' comments marked a "serious precedent" in sanctioning killing, glorifying murderers and insulting al-Zarqawi's Jordanian victims.
Parliament, which is in recess for the summer, did not say if it will take action against the four lawmakers, whose party, with 17 MPs, is the political arm of the Muslim Brotherhood Movement.
On Sunday evening, the four MPs - Abu Fares, Jaafar al-Hourani, Ali Abu Sukkar and Ibrahim al-Mashwakhi - who visited al-Zarqawi family were arrested, the leader of their party, Hamza Mansour, said.
A US air raid killed al-Zarqawi
But a security source said the MPs were only brought in for questioning and could not be arrested because of their parliamentary immunity.
Three of them are from al-Zarqawi's hometown of Zarqa, 22km east of the capital, Amman.
The remarks and the visit to al-Zarqawi's home have riled Jordanian public opinion.
Many in the kingdom detest the Jordanian-born al-Qaida in Iraq leader for claiming responsibility for the hotel bombings that killed 60 civilians, including women and children attending a wedding.
"We strongly denounce and condemn MPs Ibrahim Mashukhi, Mohammed Abu Fares, Ali Abu Sukkar and Jaafar Horani ... for presenting their condolences for the so-called martyr," the families said in a statement.
They expressed outrage over Abu Fare's description of "the criminal (al-Zarqawi) as a martyr".
Al-Zarqawi himself was killed on Wednesday in a US air raid north of Baghdad. He has been blamed for the grisly beheadings of hostages and the killings of thousands in suicide bombings.
Jordan's parliament blasted the Islamist deputies "for presenting condolences to a terrorist", state-run Petra news agency reported.
Newspaper columnists and editorials continued their scathing attacks on Sunday against the Islamic Action Front, Jordan's largest opposition group.
Abu Fares' remarks "broke the trust of a large segment of the Jordanian people" in the Islamic Action Front, declared the independent Ad-Dustour in a front-page editorial.
Even ordinary Jordanians, including tribal leaders, businessmen and professionals, condemned the four members of the Islamist party in dozens of advertisements published in Jordanian dailies.
Mamdouh Abbadi, a pro-government MP, said deputies may consider unspecified measures to "reprimand" the four Islamist lawmakers. He declined to elaborate.
The MPs, meanwhile, were quoted by the Jordanian media as saying they visited the al-Zarqawi family in Zarqa out of solidarity and in keeping with tribal and religious traditions.
"We did not go to make a political stand. It is our duty to support al-Zarqawi's family at this time," Abu Sukkar was quoted as saying.
Al-Zarqawi's elder brother, Sayel, on Thursday began receiving condolences at his home from well-wishers in accordance with Muslim tradition.
"Martyrdom of the hero Abu Musab al-Zarqawi," read a banner draped across the family's street in the Maasum neighbourhood of Zarqa.