Mr Thabane, who has been in a fractious coalition government with his political rival Mr Metsing, left for neighbouring South Africa on Saturday after the army surrounded his residence and police stations in Lesotho's capital Maseru and gunshots rang out.
One policeman was shot dead and four others were wounded during the confrontation, according to police senior superintendent Mofokeng Kolo.
The army denied trying to force the prime minister out of power, saying it had moved against police officers suspected of planning to arm a political faction in the small southern African kingdom.
Diplomats in Maseru said the army was largely seen as loyal to the deputy prime minister, while the police force largely supported the prime minister.
Regional power South Africa condemned the army's actions and later invited the deputy prime minister to talks.
Lesotho's Communications Minister Selibe Mochoboroane said: "Constitutionally, in the absence of the prime minister, the deputy prime minister takes the reins.
"The deputy will still oversee other issues that need to be taken care of until the prime minister returns."