Mr Chavez is in hospital in Cuba after cancer surgery, and has suffered complications caused by a lung infection.
Legislators voted to give Mr Chavez as much time as he needs to recover.
He has not been seen in public since his last operation a month ago.
The government insists that the inauguration is a mere formality for an incumbent leader and can take place at a so far unspecified later date.
The opposition argues that Mr Chavez’s current mandate expires on 10 January and is calling on the Supreme Court to rule on the issue.
The court has scheduled a news conference at 14:00 GMT on Wednesday.
“Right now in Venezuela, without any doubt whatsoever, a constitutional conflict has arisen,” opposition leader Henrique Capriles said.
The opposition also argues that Vice-President Nicolas Maduro’s mandate ends on 10 January so he cannot take over as leader; instead the current Speaker of the National Assembly, Diosdado Cabello, should act as caretaker president.
President Chavez, who has been in power since 1999, was re-elected in October for a fourth term.
Show of support
After weeks of speculation, Mr Cabello announced to legislators that Mr Chavez had requested to be sworn in at a later date before the Supreme Court, according to Article 231 of the Constitution.
“On the recommendation of his medical team, the process of post-operation recuperation will have to be prolonged beyond 10 January, [as a result of which] he will be unable to present himself on this date to the National Assembly.” he said, reading a letter from Mr Maduro.
On Monday, Mr Cabello called on Chavez supporters to take to the streets of Caracas on Thursday to show support for him.
He said several foreign leaders had agreed to be at the Miraflores Presidential Palace on inauguration day.
But Mr Capriles urged them to stay away and not succumb to “a game by a political party”, referring to Mr Chavez’s Socialist Party (PSUV).
In his most recent update on Mr Chavez, Information Minister Ernesto Villegas said his condition was “stable”, and he was “responding to the treatment”.
Source: BBC
