Tania D'Amelio, an official of the National Electoral Council (CNE), said nominations would be accepted through Monday. The council will announce which nominations are accepted by Thursday.
Opposition politicians have accused the CNE of being under the thumb of President Nicolas Maduro.
The presidential elections, with Maduro seeking a new term that would keep him in office until 2025, are traditionally held in December. They were moved forward by the ruling Constituent Assembly, which is controlled by the governing party.
Maduro called Wednesday for snap legislative elections for the National Assembly, proposing to bring them forward by nearly two years to coincide with the April 22 poll. And he hit back at the opposition MUD coalition, which had said it would not take part in the early elections without guarantees they would be free and fair.
"We are going to (hold) the elections come rain, shine or lightning, with or without the MUD," said Maduro.
But the United States, which under President Donald Trump has been deeply critical of Maduro's leadership in crisis-torn and economically suffering Venezuela, on Saturday rejected the call for an early legislative vote.
"We reject ruling party calls to replace the democratically elected National Assembly simultaneously, rather than in 2021, as provided for under the 1999 Constitution," said a State Department statement.
"Deepening the rupture of Venezuela's constitutional and democratic order will not solve the nation's crises."
The statement called for "a free and fair election" involving full participation of all political leaders, the immediate release of all political prisoners, credible international observation and an independent electoral authority.
The opposition Democratic Unity Roundtable (MUD) said Wednesday it would not register presidential candidates, believing there were no guarantees of transparency. But it left the door open to taking part if conditions were improved.
Delcy Rodriguez, president of the Constituent Assembly, has said that that body will consider possible dates for the legislative vote when it meets next week.
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