Nepal's foreign ministry said four local people were injured yesterday when SSB personnel opened fire at them.
The incident occurred when residents of Sunsari district which lies on the Nepal-India border were burning firewood.
Nepal alleged that the SSB had entered Nepalese territory and fired at the four Nepalese nationals while chasing a group of chemical fertiliser smugglers.
The Ministry of Foreign Affairs here said in a press release that its "serious attention" has been drawn to the incident that occurred yesterday at around 6:20 am, 100 metres inside Nepalese territory in Sunsari district when the four Nepalese were injured by bullets fired by SSB personnel.
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It asked Indian authorities for an early investigation into the incident and strong action against those involved and urged India to check such actions in future.
The ministry also requested India to share the findings of the investigation.
India had yesterday hit out at Nepal for "shifting" blame of atrocities inside its "volatile" Sunsari district to the SSB after Kathmandu alleged that the Indian border force shot four Nepalese on charges of smuggling chemical fertilisers.