The group of about 21 relatives was stopped by the police from entering the building where Najib and top Malaysian-Chinese officials were celebrating the start of the year of the goat.
The relatives called on the Malaysian government to retract its declaration that the aircraft was lost and all those aboard were officially dead.
The group stood outside the building, some were crying and some fainted.
They carried banners with the Chinese characters for "peace, justice and hope." Police allowed them to join the party after Najib and other officials left.
Late Wednesday, the group gathered outside the prime minister's office in the federal government centre of Putrajaya, but Najib was not around and an aide received the Chinese calligraphy scrolls they wanted to give to the Malaysian leader.
The relatives arrived in Kuala Lumpur earlier this month to seek answers about the disappearance of the aircraft.
They were able to meet with the chief of Malaysia Airlines.