Mother Teresa's remains are in India and King Ahmet Zog's in France. Prime Minister Sali Berisha's government has asked India for the Roman Catholic nun's to be returned by the 100th anniversary of her birth in August.
Berisha said Albania has started negotiations with India's government, which "will be intensified this year."
Macedonia and Albania have been engaged in a dispute over the national identity of Mother Teresa, who was born in Macedonia to an ethnic Albanian family. She went to Calcutta, India, in 1929, and dedicated herself to the service of the poor and infirm, receiving the Nobel Peace Prize in 1979.
After her death in 1997, she was buried in Calcutta and Pope John Paul II beatified her in 2003. Albania's main airport outside the capital, Tirana, is named after Mother Teresa.
Zog was the small Balkan country's first _ and only _ post-independence monarch, reigning from 1928 to 1939, when he fled after Albania's occupation by fascist Italy. He died in France in 1961, and is buried at the Thiais Cemetery near Paris.
"The Albanian government took this decision recognizing Ahmet Zog ... as one of the greatest, most distinguished personalities with a major contribution in the history of the Albanian nation," Berisha told a news conference.
Berisha said the king's remains would be re-interred at the former Albanian royal family's private cemetery near Tirana, without specifying when that was expected.
There has been no reaction from the royal family or French authorities.
Albania's communist rulers abolished the monarchy in 1946, but the exiled royals insisted that Zog's son Leka Zog I was the country's legitimate ruler.
Since the fall of Communism in 1991, Albania has been a parliamentary republic. A small royalist party is allied to Berisha's 16-party governing Democrats' coalition.
Albanians voted against restoring the monarchy in a 1997 referendum.