The two killed were among tens of thousands of refugees who headed for Kakaribhitta, 700 km east of Kathmandu on the Nepal-India border, in what they called "The Long March Home". They have been trying to reach Bhutan via India since Sunday.
"The situation is getting worrisome as more refugees have vowed to enter India to reach Bhutan," local human rights activist Arjun Basnet told IRIN. He said on Wednesday, nearly 50,000 refugees from Beldangi refugee camps were planning to join the demonstration near Mechi Bridge in Kakaribhitta.
Leading the demonstration were about 15,000 refugees from five camps in the Goldhap area, human rights activist said.
To control the refugees, around 7,000 armed Indian police of the Sashastra Seema Bal (SSB) are on high alert and standing guard around the bridge and throughout the border area.
Nepal's Home Ministry asked the refugees on Wednesday to return to their respective camps, but in vain.
"Considering the sensitivity of the border areas, the government of Nepal requests the Bhutanese refugees not to do anything that will raise tension and chaos, and maintain peace and order by returning to their camps and to show respect for refugee norms," said Home Minister Krishna Prasad Sitaula.
The government has also sent a team led by Jhapa's chief district officer, Jaya Mukunda Khanal, to India for talks to settle the unrest. Nepal's political party leaders as well as Bhutanese refugee leaders have joined the team.
"Huge tragedy" warning
"There will be a huge tragedy if the refugees continue their demonstration and force their way to India," said Basnet, adding that most of the demonstrators are young refugees between 15 and 18.
According to the Nepal Red Cross Society (NRCS), which is providing medical treatment to the refugees, many have been seriously injured and hospitalised in various medical centres in major towns in eastern Nepal.
Meanwhile, local communities have been providing food to the thousands of demonstrators.
"But the problem is that the border has now been sealed and even Nepalese and Indian citizens are prevented from travelling," said Basnet. To make matters worse, he added, Nepalese citizens are being victimized, as some were beaten up on Wednesday by Indian police near the border.
"We are very frustrated as the Nepalese and Bhutan governments have failed to find any solution. Even the UN has failed to resolve our problems," a local refugee, Ramesh Lama, said.
Known as Lhotsampas in Bhutan, the refugees were forcibly evicted from their homes in 1990 by the Bhutanese government, which introduced a new law stripping them of citizenship and civil rights because of their Nepalese ancestry.
Since then, the refugees have been living in seven camps in the Morang and Jhapa districts of eastern Nepal. The Bhutanese and Nepalese governments have had more than 15 rounds of unsuccessful bilateral negotiations to resolve the problem.