"Venezuela is going to ask Interpol to issue a red notice against these people involved in serious crimes," Maduro told a news conference, referring to ex-chief prosecutor Luisa Ortega and her lawmaker husband.
The couple faces court action by Maduro's allies which they have denounced as politically motivated.
They fled first to Colombia and were bound on Tuesday for Brazil, Colombian migration authorities said.
Both those countries have echoed Ortega and the United States in condemning Maduro's handling of the crisis.
Ortega, 59, was fired from her post this month after being earlier charged with misconduct by authorities loyal to Maduro.
She and her husband, German Ferrer, fled on Friday after the pro-Maduro Supreme Court issued an arrest warrant against Ferrer for alleged corruption and extortion.
The Venezuelan courts had already frozen Ortega's assets and banned her from traveling abroad.
Maduro has faced months of deadly mass protests by opponents who blame him for an economic crisis and are demanding elections to replace him.
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