Civil society activists in Sri Lanka say they fear for the lives of the men.
Police in Jaffna say they have no information about the whereabouts of the two men and are investigating.
The BBC’s Charles Haviland in Colombo says that this is just the latest in a series of disappearances in recent months.
The Asian Human Rights Commission issued a statement on Monday highlighting the latest case and calling on the government to ensure that cases of “forced disappearances” are thoroughly and effectively investigated.
Our correspondent says that for several months Mr Weeraraj and Mr Muruganathan were part of a group that had been organising protests in Colombo, bringing mothers, fathers and wives of missing people from the north to the capital to highlight their desperation.
These families are searching for relatives who disappeared during and after Sri Lanka’s civil war, which ended in 2009 after government forces defeated Tamil Tiger rebels fighting for a separate homeland.
A similar rally had been planned by the two men for the northern city of Jaffna on Saturday but before it could happen they went missing – apparently abducted while travelling by motor bike.
Mr Weeraraj had been detained and questioned about his activities and recently told the BBC he was being tracked by state security officials.
An associate of the two, Nuwan Bopage, said that because of the heavy security presence in Jaffna, the security forces must be responsible for the abductions.
But the military spokesman told the BBC that, according to his information, the security forces were not involved. The military was ready to help the police trace the missing men, he said.
The police said they had no information but were investigating.
Mr Weeraraj’s father is quoted by colleagues of the men as saying his son had received anonymous phone calls saying he would be “eliminated” from politics if he continued his political involvement in the north.
‘White van’ abductions
Separately, there are reports of at least nine other men being abducted within the past couple of months, all of them in or near the capital.
The local Sunday Times newspaper quoted eyewitnesses as saying they were bundled away in white vans – unmarked vehicles of a type used for many unexplained past disappearances.
The newspaper says one person was released, one was found dead and the others are unaccounted for. The report quotes opinions blaming the incidents on state-sponsored hit squads, drug cartels or contract killers.
Our correspondent says it appears to mark the reappearance of a trend of abductions that had diminished since the war ended two years ago.