Myanmar nationals Wa Lone, 31, and Kyaw Soe Oo, 27, were arrested a month ago after receiving documents from two policemen during a dinner in Yangon.
They were detained under the colonial-era Official Secrets Act after they left the restaurant for alleged possession of classified documents obtained "by deception".
The pair had been reporting on the military campaign in Rakhine state that has forced some 655,000 Rohingya Muslims to flee over the border to Bangladesh since August, violence the UN has condemned as ethnic cleansing.
The issue is highly sensitive inside Myanmar.
Reuters insists their reporters have done nothing wrong, while their families have suggested the pair were set up.
"A free press is critical to a free society-the detention of journalists anywhere is unacceptable," he tweeted on Monday.
"The Reuters journalists being held in Myanmar should be released immediately."
The case has cast a spotlight on Myanmar's troubled transition to democracy after nearly five decades of military rule.
It touches on both slumping press freedom and the Rohingya crisis, two issues that have raised questions over the country's ability to shake off the legacy of junta rule.
The military has severely restricted access to northern Rakhine state to journalists, aid groups and observers.
The Reuters reporters were held incommunicado for two weeks without access to lawyers, family or colleagues before a brief court appearance to extend their remand for a further two weeks.
They must either be charged at Wednesday's hearing or released.
Reuters has vociferously denied any wrongdoing on behalf of their reporters, defending their right to report on an issue of global significance.
A slew of legal cases against journalists have compounded disappointment among those hoping the civilian government of Aung San Suu Kyi would usher in a new era of freedom.
Her administration shares power with an army that still controls all security policy and other key levers of government.
Suu Kyi's time in office has also been dominated by the Rohingya crisis, with criticism pouring in from around the globe over her refusal to denounce the army's crackdown and allow in international investigators.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)