The council said that according to its latest figures, Nicolas Maduro won the election by 1.49 percentage points, or fewer than 225,000 votes.
Earlier official figures had suggested Nicolas Maduro won by 1.8 percentage points.
Opposition candidate Henrique Capriles Radonski has demanded a full recount, which the council has rejected.
Figures released by the National Electoral Council (CNE) on Monday revealed that Henrique Capriles had won 93.13% of the votes cast abroad.
With 99.79% of the votes counted, the margin between the two candidates had narrowed to 1.49 percentage points, it said.
The CNE declared President Nicolas Maduro the winner on April 15, after he had gained what it called an “irreversible majority”. He was sworn in on April 19.
Henrique Capriles has demanded a vote-by-vote recount, but the CNE said it would be legally impossible to carry out.
It has, however, agreed to carry out a partial audit, which is expected to take until June. During the audit, 56% of the votes cast will be examined.
The CNE says the remaining 44% had been checked immediately after the election.
On Monday, Henrique Capriles said Nicolas Maduro had “illegitimately stolen the presidency”.
He has until May 6 to lodge his request with the Supreme Court contesting the election result.
Henrique Capriles said he had “no doubt that this will end up before an international body”.
Supporters and opponents of Nicolas Maduro have also been clashing in Venezuela’s parliament, the National Assembly.
Opposition politicians have complained about being “silenced” by National Assembly President Diosdado Cabello.
“I am going to ask you: Mr. Deputy, do you recognize Nicolas Maduro?” Diosdado Cabello asked one of them.
“If you say no, you don’t get to speak in the assembly.”
Both Henrique Capriles and Nicolas Maduro have urged their supporters to turn out for separate demonstrations on May 1st, sparking fears the two camps could clash.
On Monday, Nicolas Maduro said he had changed the route of his march because he “did not want problems”.
But the opposition says it continues to be targeted by the government, citing the arrest on Saturday of retired General Antonio Rivero as proof.
The opposition politician has been charged with criminal instigation and criminal association, after prosecutors blamed him for outbreaks of post-election violence.
Relatives of General Antonio Rivero says he is on a hunger strike in protest.
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