One of those killed was identified as a medical worker at the hospital while the other was said to be a mason who had been working at a construction site at the hospital.
A third non-local victim was injured and is receiving treatment at the same facility.
The unrest forced business owners in the border town to close shop for the whole of Thursday.
“We have come here to condole with families that lost their loved ones in the hands of security officers, not to incite anyone against anybody,” said Mr Adan.
The MP denied claims that locals were incited to attack non-locals to avenge the killing of the three in Elram.
Mr Adan Mohamed Noor, an Eala MP, called on local security agents to find the perpetrators of both incidents and charge them.
“Let security officers investigate, arrest and charge anyone involved in these incidents,” he said.
Police and military personnel were forced to go round Elwak town to pick non-locals from their residences and places of work and take them to safety.
“We are assembling all non-locals because we are not sure of what will happen tonight. It is better to watch them closely," said an officer involved in the operation.
The non-locals were attacked by people who retaliated following Mr Adow's shooting and the killing of the three relatives.
“We are put in the same basket as police any time a local is injured or killed by security agents in this part of the country,” lamented one Jackline Auma.
Mr Matabeyi Kembeyi, Mandera South Deputy County Commissioner, declined to comment on the two incidents but said his office was aware of planned demonstrations and would stop them.