JERUSALEM — Israel arrested two Palestinian legislators affiliated with Hamas as they staged a protest in the offices of the International Committee of the Red Cross in East Jerusalem on Monday, an act criticized by the Palestinian leadership as a blow to the first direct meetings between the Israeli and Palestinian sides in more than a year now under way in Jordan.

At the same time, the prime minister of Israel, Benjamin Netanyahu, called on the leaders of the Palestinian Authority to condemn remarks by its top cleric, Sheikh Muhammad Hussein, who recently recited an ancient Islamic text at a ceremony broadcast on Palestinian Authority television advising that Judgment Day will come only when the Muslims fight and kill the Jews.

“Whoever wants peace should not permit such incitement and should not allow calls to murder Jews,” Mr. Netanyahu said Monday.

The latest developments reflected a worsening atmosphere as the two sides approached a critical juncture in the meetings being held under the auspices of the Jordanians and the so-called quartet of Middle East peacemakers, made up of the United States, the European Union, Russia and the United Nations.

Israeli and Palestinian representatives met Saturday for the fourth time this month as part of an international effort to get peace negotiations, stalled since September 2010, back on track. The Palestinians say they will not resume formal peace talks unless Israel stops settlement building, while the Israelis have called for talks without preconditions.

Palestinian officials have reported little progress in the preliminary discussions and have threatened to stop the talks if Israel does not outline comprehensive proposals on borders and security by Jan. 26, echoing a request made Oct. 26 by the quartet for both sides to produce such proposals within three months. Israel says the three-month period only started once the sides met Jan. 3, and that the deadline therefore is in April. The international participants are interested in extending the discussions beyond this week, regardless, and have repeatedly called on both sides to refrain from provocative actions.

But that has done little to keep both sides from escalating tensions.

The mufti of Jerusalem, Sheikh Hussein, addressed a crowd at an event marking the 47th anniversary of the founding of Fatah, the mainstream movement led by the Palestinian Authority president, Mahmoud Abbas. He quoted a hadith, a saying attributed to the Prophet Muhammad, stating: “The Hour will not come until you fight the Jews. The Jews will hide behind stones or trees. Then the stones or trees will call: Oh Muslim, servant of Allah, there is a Jew behind me, come and kill him.”

Israeli police officers and undercover units entered the Red Cross headquarters in East Jerusalem Monday afternoon and arrested Muhammad Totah, a member of the Palestinian Legislative Council, and Khaled Abu Arafeh, a former minister, as they were sitting in a tent set up as part of a protest they were conducting in the yard.

Mr. Totah, Mr. Abu Arafeh and a third Hamas legislator, Ahmed Attoun, entered the Red Cross premises in July 2010 and staged a sit-in after the Israeli authorities stripped them of their Jerusalem residency papers and ordered them out of the city. Mr. Attoun was arrested in September 2011 and was expelled to the West Bank in December, but the others have been at the Red Cross ever since.

Israel occupied the eastern part of the city after conquering it from Jordan in the 1967 war, then annexed it in a move that has not been internationally recognized.

A police spokesman, Micky Rosenfeld, said that the two legislators arrested were suspected of carrying out Hamas activities in Jerusalem. The Islamic militant group is considered an illegal organization by Israel.

Cecilia Goin, a spokeswoman for the International Committee of the Red Cross, said by telephone that the organization had informed the three from the start that they could stay on the premises, but that the Red Cross did not enjoy diplomatic immunity and could not prevent the Israeli authorities from arresting them. The organization had also informed the Israeli authorities that the three were on the premises, she said.

The three received relatives and other visitors in the protest tent for much of the day and were given the use of one room inside the Red Cross building where they slept at night.

Monday’s arrests came days after Israeli forces in the West Bank arrested Aziz Dweik, the speaker of the long-defunct Palestinian Parliament. Mr. Dweik was released from an Israeli prison in 2009 after serving nearly three years for belonging to an illegal organization.

Hamas called on the Palestinian Authority leaders to cease contacts with the Israelis after Mr. Dweik’s rearrest, and the Palestinian negotiators submitted a letter calling on Israel to release Mr. Dweik and more than 20 other Hamas legislators in Israeli detention, along with prisoners arrested before the Israeli-Palestinian accords of May 1994, women and others.

Saeb Erekat, the chief Palestinian negotiator, said in a statement that the detention of Mr. Totah and Mr. Abu Arafeh 24 hours later was a “flagrant act of aggression.”

Mr. Netanyahu described the words of the mufti of Jerusalem, Sheikh Hussein, as “morally heinous” and compared the remarks to those of Haj Amin al-Husseini, the grand mufti of Jerusalem who notoriously aligned himself with Hitler in the 1930s. Palestinian television broadcast the mufti’s comments on Jan. 9 and Palestinian Media Watch, an Israeli monitoring group, drew attention to them on Jan. 15. An Israeli official said that the prime minister became aware of it only in the past few days.

The mufti denied calling for the killing of Jews, telling Israel Radio on Sunday that he was only quoting the words of the Prophet Muhammad. He told Voice of Palestine radio on Monday that “these allegations come within the Israeli incitement campaign against Jerusalem and its figures.”