Amid swirling rumours about Mr Meles' health, officials said on Thursday that the 57-year-old premier was "stable", but that he has been told to take some leave.
On paper the Meles government has fostered a policy of ethnic federalism, devolving significant powers to regional, ethnically-based authorities but central control remains firmly in the hands of the ruling party.
The position of president is largely honorific and Mr Meles, a former rebel fighter who has been in power for more than two decades, holds the real political power.
According to Ethiopia's constitution, the deputy prime minister is obliged to "act on behalf of the Prime Minister in his absence."
But the law does not specify whether the deputy takes over the premier's full responsibilities and does not say what happens if the prime minister is absent for a prolonged period or is no longer able to rule.
"I don't think there's any sort of contingency in place for Meles not being in power," said Ahmed Soliman, Horn of Africa research assistant at British think tank Chatham House.
Diplomats and analysts here say it is not clear how the government is being run while Mr Meles, who has been in power since 1991, is away.
"We have no more information than what we are getting from (the media)," said one diplomat, speaking on condition of anonymity.
Another diplomat said that it is not clear how much decision-making power Deputy Prime Minister Hailemariam Desalegn wields.
"He is obviously subbing for the prime minister... but what the legal position is, I don't know," the second diplomat said.
Mr Soliman said despite Mr Hailemariam's official role, the prime minister is likely retaining control behind the scenes.
Mr Hailemariam, 47, is currently in China for a summit, but is expected back in the country soon, according to government spokesman Bereket Simon.
Diplomats and analysts say there have been no signs of any moves so far within the ruling party to grab power and there is no indication of any fracture with the ruling party.
Mr Bereket said the government "system is functional and working" and that Mr Meles remains available to senior government officials when they need him.
He said there is no need for a long-term succession plan because Mr Meles is expected back in office in a matter of days.
Diplomats in Brussels however said this week that Mr Meles, who was last seen in public in June, was in hospital there in a "critical" condition.
Ethiopian officials have not said what Mr Meles is suffering from or where he is being treated.
Mr Meles missed an African Union summit hosted in the Ethiopian capital last weekend, which prompted speculation over the former Marxist rebel's health.
Mr Meles, who toppled the bloody dictatorship of Mengistu Haile Mariam in 1991, has said he will stand down at the end of his current term in 2015. No clear successors have been primed, but Mr Bereket told reporters Thursday the ruling party has been saying a "new batch of leaders should come so that they should receive the baton."
Mr Soliman said he expects the ruling party to maintain its iron grip on the country and does not expect the party to diverge from Meles' policies during his sick leave.
"Short term absence isn't going to change that," he said.