With medals of honor and ceremonies thousands of miles apart, France and Israel paid tribute Tuesday to those killed in the Paris terrorist attacks.

At police headquarters in Paris, French President Francois Hollande paid separate tribute Tuesday to the three police officers killed in the attacks, placing Legion of Honor medals on their caskets.

"They died so that we could live free," he said, flanked by hundreds of police officers.

Hollande vowed that France will be "merciless in the face of anti-Semitic, anti-Muslims acts, and unrelenting against those who defend and carry out terrorism, notably the jihadists who go to Iraq and Syria."

As Chopin's funeral march played in central Paris and the caskets draped in French flags were led from the building, a procession began in Jerusalem for the four Jewish victims of the attack Friday on a kosher supermarket in Paris.

"Returning to your ancestral home need not be due to distress, out of desperation, amidst destruction, or in the throes of terror and fear," said Israeli President Reuven Rivlin. "Terror has never kept us down, and we do not want terror to subdue you. The Land of Israel is the land of choice. We want you to choose Israel, because of a love for Israel."

Prime Minister Benjamin Netanyahu and other public figures gathered in Jerusalem to attend the rites for Yohan Cohen, Yoav Hattab, Francois-Michel Saada and Phillipe Braham, who died during a tense hostage standoff at the market on the eastern edge of Paris.

The four were among 17 people killed in a wave of terror attacks carried out over three days last week by militants claiming allegiance to Al Qaeda and the Islamic State extremist groups.

The killings shocked France's 500,000 strong Jewish community -- the largest in Europe -- and prompted calls from Netanyahu for Jews throughout the continent to immigrate to Israel following what he called a "rising tide of anti-Semitism."

In a statement Sunday from Paris, Netanyahu said he had "acceded to the request of the families of the victims of the murderous terror attack" and instructed the government to help bring the bodies to Israel. Early Tuesday, the bodies of the four arrived at Ben Gurion International Airport outside of Tel Aviv early Tuesday. From there they were taken to Jerusalem for the funeral rites.

But Netanyahu's calls for immigration of French Jews appeared to have sparked tensions with French political leaders, including President Francois Hollande, who attended a memorial service for the four at a Paris synagogue on Sunday night, but left the event before Netanyahu addressed it.

Also, many French Jews, including the country's chief rabbi, have not been enthusiastic over Israeli attempts to suggest that Israel and not France is their natural home.

Hollande and French leaders take pride in the inclusiveness of the French republic and see in its continuing ability to nurture its Jewish population a litmus test of the republic's legitimacy.

France is the first country in Europe to have accorded Jews full civil rights, in the immediate wake of the 1789 revolution. Two French Jews -- Leon Blum and Pierre Mendes-France -- have served as French premiers.

In an interview published late last week in the Atlantic, current French Premier Manuel Walls said that if 100,000 French Jews left the country "France will no longer be France. The French Republic will be judged a failure."

But those sentiments have little resonance in Israel, where a national ethos has been built around the notion that the country is the only place in the world where Jews can feel secure.  Leaders from across the political spectrum have traditionally encouraged Jewish immigration from around the world.

Last year, France topped the immigration list to Israel, according to the Jewish Agency, a nonprofit group that works closely with the government and acts as a link for Jews around the world. Nearly 7,000 new immigrants came in 2014, double the number from the previous year.

Jewish community leaders in France have said that all of the victims of Friday's attack had close ties to Israel.

Cohen, 22, worked at the kosher grocery store attacked by Amedy Coulibaly. He was friends on Facebook with his colleague Lassana Bathily, a Muslim who saved the lives of shoppers by turning off the stockroom's freezer and hiding them inside before sneaking out through a fire escape to brief police on the hostage-taker upstairs.

Hattab finished high school in Tunisia before moving to Paris to seek a business degree in marketing. He was killed while attempting to snatch one of Coulibaly's weapons, according to witnesses quoted in French media. The 21-year-old Hattab was the son of Tunis' chief rabbi.

Saada, a pensioner in his 60s, was killed while buying goods for the Sabbath. Born in Tunis, he left a wife and two children, both Israeli residents.

Philippe Braham, a sales manager in his 40s, was the brother of a rabbi of a suburban Paris synagogue, according to French daily Le Parisien.

The Associated Press contributed to this report.